Statistics

Problem Statement for "BoardCoveringDiv1"

Problem Statement

Lucyanna loves puzzles and she is always eager to invent new ones. She has recently invented a puzzle based on placing trominoes onto a square board.

The board is divided into a grid of unit squares. One of the unit squares on the board is black, all others are white.

A tromino is any connected piece that exactly covers three unit squares of the board. (Trominoes come in two shapes: "L" and "I".)

The goal of the puzzle is to cover all white squares of the board using trominoes. More precisely, the rules for Lucyanna's puzzle are as follows:

  • The player must place some trominoes onto the board.
  • Each tromino must exactly cover three unit squares of the board. (Thus, each tromino must lie completely inside the board.)
  • Each white unit square must be covered by exactly one tromino. (Thus, the trominoes cannot overlap.)
  • The black square must remain uncovered.

You are given the ints N, R and C. Your task is to find any valid solution for a N times N board on which the black square is in row R, column C. (Both indices are 0-based.) Once you have a solution, you need to color its trominoes using 10 non-black colors in such a way that adjacent trominoes always have different colors. (Trominoes are adjacent if they share a side of a unit square. You may assume that any valid solution can be colored in this way.)

If there are no solutions for the given N, R and C, return an empty String[]. Otherwise, return a String[] with R elements, each containing C characters. Use the characters '0'-'9' for the ten tromino colors and the character '#' for the uncovered black square.

Definition

Class:
BoardCoveringDiv1
Method:
make
Parameters:
int, int, int
Returns:
String[]
Method signature:
String[] make(int N, int R, int C)
(be sure your method is public)

Constraints

  • N will be between 1 and 47, inclusive.
  • R will be between 0 and N-1, inclusive.
  • C will be between 0 and N-1, inclusive.

Examples

  1. 1

    0

    0

    Returns: {"#" }

  2. 2

    1

    1

    Returns: {"00", "0#" }

  3. 3

    0

    2

    Returns: { }

  4. 3

    1

    0

    Returns: { }

  5. 3

    1

    1

    Returns: { }

  6. 4

    0

    0

    Returns: {"#011", "0021", "1220", "1100" }

  7. 4

    3

    2

    Returns: {"2211", "2331", "0300", "00#0" }

  8. 4

    1

    2

    Returns: {"1100", "12#0", "0221", "0011" }

  9. 5

    4

    4

    Returns: {"11222", "10011", "20221", "21200", "2110#" }

  10. 5

    0

    1

    Returns: {"0#001", "00301", "13321", "11220", "33300" }

  11. 5

    3

    3

    Returns: {"11222", "10011", "20221", "212#0", "21100" }

  12. 5

    4

    2

    Returns: {"33300", "22110", "23312", "03002", "00#02" }

  13. 5

    2

    1

    Returns: {"11002", "12202", "0#212", "00110", "22200" }

  14. 5

    2

    2

    Returns: {"00112", "02212", "12#02", "11001", "22211" }

  15. 7

    0

    6

    Returns: {"000110#", "2221200", "1110221", "2220011", "0002120", "1112120", "0002120" }

  16. 7

    1

    0

    Returns: {"0011000", "#031222", "0332000", "0022111", "1203000", "1203111", "1203000" }

  17. 7

    1

    1

    Returns: {"0011000", "0#21222", "1220111", "1100222", "0212000", "0212111", "0212000" }

  18. 7

    2

    0

    Returns: {"0022000", "0332111", "#031000", "0011222", "1202000", "1202111", "1202000" }

  19. 7

    4

    5

    Returns: {"0002021", "1112021", "0002021", "2221100", "00012#0", "2220221", "1110011" }

  20. 7

    2

    2

    Returns: {"0011000", "0221222", "12#0111", "1100222", "0212000", "0212111", "0212000" }

  21. 7

    3

    6

    Returns: {"1110011", "2220221", "0001200", "222110#", "0002010", "1112010", "0002010" }

  22. 7

    5

    3

    Returns: {"0123000", "0123111", "0123000", "2200222", "2330111", "130#000", "1100111" }

  23. 7

    4

    3

    Returns: {"0212000", "0212111", "0212000", "1100111", "130#000", "2330222", "2200111" }

  24. 7

    3

    3

    Returns: {"0011000", "0221222", "1200111", "110#000", "0212111", "0212000", "0212111" }

  25. 47

    23

    23

    Returns: {"11132010101010101010101010101010101010101010111", "00032010101010101010101010101010101010101010222", "11132010101010101010101010101010101010101010111", "00011132010101010101010101010101010101020121000", "11100032010101010101010101010101010101020121222", "00011132010101010101010101010101010101020121000", "11100011132010101010101010101010101010111000111", "00011100032010101010101010101010101010222111000", "11100011132010101010101010101010101010111000111", "00011100011132010101010101010101020121000111000", "11100011100032010101010101010101020121222000111", "00011100011132010101010101010101020121000111000", "11100011100011132010101010101010111000111000111", "00011100011100032010101010101010222111000111000", "11100011100011132010101010101010111000111000111", "00011100011100011132010101020121000111000111000", "11100011100011100032010101020121222000111000111", "00011100011100011132010101020121000111000111000", "11100011100011100011132010111000111000111000111", "00011100011100011100032010222111000111000111000", "11100011100011100011132010111000111000111000111", "00011100011100011100011222000111000111000111000", "11100011100011100022210011222000111000111000111", "00011100011100011100020#21000111000111000111000", "11100011100011100011121220111000111000111000111", "00011100011100011100021100222111000111000111000", "11100011100011100012102012000222111000111000111", "00011100011100022212102012111000222111000111000", "11100011100011100012102012000111000222111000111", "00011100011100011101010101212000111000222111000", "11100011100011122201010101212111000111000222111", "00011100011100011101010101212000111000111000222", "11100011100012102010101010101212000111000111000", "00011100022212102010101010101212111000111000111", "11100011100012102010101010101212000111000111000", "00011100011101010101010101010101212000111000111", "11100011122201010101010101010101212111000111000", "00011100011101010101010101010101212000111000111", "11100012102010101010101010101010101212000111000", "00022212102010101010101010101010101212111000111", "11100012102010101010101010101010101212000111000", "00011101010101010101010101010101010101212000111", "11122201010101010101010101010101010101212111000", "00011101010101010101010101010101010101212000111", "12102010101010101010101010101010101010101212000", "12102010101010101010101010101010101010101212111", "12102010101010101010101010101010101010101212000" }

  26. 6

    3

    2

    Returns: { }

  27. 45

    31

    32

    Returns: { }

  28. 16

    0

    12

    Returns: {"111000111000#011", "0001110001110021", "1110001110001220", "0001110002221100", "1110001110002021", "0001110001112021", "1110001110002021", "0001110003210210", "1110001113210210", "0001110003210210", "1110003210102101", "0001113210102101", "1110003210102101", "0003210101021010", "1113210101021010", "0003210101021010" }

  29. 14

    13

    13

    Returns: {"11132010101010", "00032010101010", "11132010101010", "00011132010101", "11100032010101", "00011132010101", "11100011132010", "00011100032010", "11100011132010", "00011100011222", "11100022210011", "00011100020221", "11100011121200", "0001110002110#" }

  30. 41

    0

    14

    Returns: {"00011100011100#02000111000111000111000111", "11100011122203002111000111000111000111000", "00011122200023312000111000111000111000111", "11122200011122110111000111000111000111000", "22200011100033300222111000111000111000111", "00011100011101012000222111000111000111000", "11100011122201012111000222111000111000111", "00011100011101012000111000222111000111000", "11100011100020120121000111000222111000111", "00011100011120120121222000111000222111000", "11100011100020120121000111000111000222111", "00011100032101201010111000111000111000222", "11100011132101201010222111000111000111000", "00011100032101201010111000111000111000111", "11100012101010120102000111000111000111000", "00022212101010120102111000111000111000111", "11100012101010120102000111000111000111000", "00011101010101012010123000111000111000111", "11122201010101012010123111000111000111000", "00011101010101012010123000111000111000111", "11100020101010120101010121000111000111000", "00011120101010120101010121222000111000111", "11100020101010120101010121000111000111000", "00032101010101201010101010111000111000111", "11132101010101201010101010222111000111000", "00032101010101201010101010111000111000111", "12101010101010120101010102000111000111000", "12101010101010120101010102111000111000111", "12101010101010120101010102000111000111000", "01010101010101012010101010123000111000111", "01010101010101012010101010123111000111000", "01010101010101012010101010123000111000111", "10101010101010101201010101010123000111000", "10101010101010101201010101010123111000111", "10101010101010101201010101010123000111000", "01010101010101010120101010101010123000111", "01010101010101010120101010101010123111000", "01010101010101010120101010101010123000111", "10101010101010101012010101010101010123000", "10101010101010101012010101010101010123111", "10101010101010101012010101010101010123000" }

  31. 23

    22

    15

    Returns: {"00032101012010101010101", "11132101012010101010101", "00032101012010101010101", "11100032101201010101010", "00011132101201010101010", "11100032101201010101010", "00011100020120101010121", "11100011120120101010121", "00011100020120101010121", "11100011102012010102000", "00011122202012010102111", "11100011102012010102000", "00011100011120101020111", "11100011100020101020222", "00011100011120101020111", "22200011100012012111000", "11122200022212012000111", "00011122200012012111000", "11100011122200333000111", "00011100011102211222000", "11100011100012331000222", "00011100022210300222111", "111000111000100#0111000" }

  32. 20

    19

    0

    Returns: {"01010101010101023111", "01010101010101023000", "01010101010101023111", "10101010101023111000", "10101010101023000111", "10101010101023111000", "01010101023111000111", "01010101023000111000", "01010101023111000111", "10101023111000111000", "10101023000111000111", "10101023111000111000", "01023111000111000111", "01023000111000111000", "01023111000111000111", "22211000111000111000", "11001222000111000111", "12202000111000111000", "00212111000111000111", "#0112000111000111000" }

  33. 13

    3

    12

    Returns: {"1110001110011", "0001112220221", "1112220001200", "222000222110#", "0001110002010", "1110001112010", "0001110002010", "1110003210101", "0001113210101", "1110003210101", "0003210101010", "1113210101010", "0003210101010" }

  34. 29

    0

    0

    Returns: {"#0112000111000111000111000111", "00212111000111000111000111000", "12202000111000111000111000111", "11001222000111000111000111000", "22211000111000111000111000111", "01023111000111000111000111000", "01023000111000111000111000111", "01023111000111000111000111000", "10101023111000111000111000111", "10101023000111000111000111000", "10101023111000111000111000111", "01010101023111000111000111000", "01010101023000111000111000111", "01010101023111000111000111000", "10101010101023111000111000111", "10101010101023000111000111000", "10101010101023111000111000111", "01010101010101023111000111000", "01010101010101023000111000111", "01010101010101023111000111000", "10101010101010101023111000111", "10101010101010101023000111000", "10101010101010101023111000111", "01010101010101010101023111000", "01010101010101010101023000111", "01010101010101010101023111000", "10101010101010101010101023111", "10101010101010101010101023000", "10101010101010101010101023111" }

  35. 32

    31

    14

    Returns: {"01010101010101012010101010123000", "01010101010101012010101010123111", "01010101010101012010101010123000", "12101010101010120101010102000111", "12101010101010120101010102111000", "12101010101010120101010102000111", "00032101010101201010101010111000", "11132101010101201010101010222111", "00032101010101201010101010111000", "11100020101010120101010121000111", "00011120101010120101010121222000", "11100020101010120101010121000111", "00011101010101012010123000111000", "11122201010101012010123111000111", "00011101010101012010123000111000", "11100012101010120102000111000111", "00022212101010120102111000111000", "11100012101010120102000111000111", "00011100032101201010111000111000", "11100011132101201010222111000111", "00011100032101201010111000111000", "11100011100020120121000111000111", "00011100011120120121222000111000", "11100011100020120121000111000222", "00011100011101012000111000222111", "11100011122201012111000222111000", "00011100011101012000222111000111", "22200011100033300222111000111000", "11122200011122110111000111000111", "00011122200023312000111000111000", "11100011122203002111000111000111", "00011100011100#02000111000111000" }

  36. 32

    0

    9

    Returns: {"111000100#0111000111000111000111", "00022210300222111000111000111000", "11100012331000222111000111000111", "00011102211222000222111000111000", "11122200333000111000222111000111", "22200012012111000111000222111000", "00022212012000111000111000222111", "11100012012111000111000111000222", "00011120101020111000111000111000", "11100020101020222111000111000111", "00011120101020111000111000111000", "11102012010102000111000111000111", "22202012010102111000111000111000", "11102012010102000111000111000111", "00020120101010121000111000111000", "11120120101010121222000111000111", "00020120101010121000111000111000", "12101012010101012111000111000111", "12101012010101012000111000111000", "12101012010101012111000111000111", "01010101201010101023111000111000", "01010101201010101023000111000111", "01010101201010101023111000111000", "10101010120101010101023111000111", "10101010120101010101023000111000", "10101010120101010101023111000111", "01010101012010101010101023111000", "01010101012010101010101023000111", "01010101012010101010101023111000", "10101010101201010101010101023111", "10101010101201010101010101023000", "10101010101201010101010101023111" }

  37. 43

    42

    38

    Returns: {"0003210101010101010101010101010101010101010", "1113210101010101010101010101010101010101010", "0003210101010101010101010101010101010101010", "1110003210101010101010101010101010101010101", "0001113210101010101010101010101010101010101", "1110003210101010101010101010101010101010101", "0001110003210101010101010101010101010101010", "1110001113210101010101010101010101010101010", "0001110003210101010101010101010101010101010", "1110001110003210101010101010101010101010101", "0001110001113210101010101010101010101010101", "1110001110003210101010101010101010101010101", "0001110001110003210101010101010101010101010", "1110001110001113210101010101010101010101010", "0001110001110003210101010101010101010101010", "1110001110001110003210101010101010101010101", "0001110001110001113210101010101010101010101", "1110001110001110003210101010101010101010101", "0001110001110001110003210101010101010101010", "1110001110001110001113210101010101010101010", "0001110001110001110003210101010101010101010", "1110001110001110001110003210101010101010101", "0001110001110001110001113210101010101010101", "1110001110001110001110003210101010101010101", "0001110001110001110001110003210101010101010", "2220001110001110001110001113210101010101010", "1112220001110001110001110003210101010101010", "0001112220001110001110001110003210101010101", "1110001112220001110001110001113210101010101", "0001110001112220001110001110003210101010101", "2220001110001112220001110001110003210101010", "1112220001110001112220001110001113210101010", "0001112220001110001112220001110003210101010", "1110001112220001110001112220001110002010121", "0001110001112220001110001112220001112010121", "1110001110001112220001110001112220002010121", "0001110001110001112220001110001112220102000", "1110001110001110001112220001110001110102111", "0001110001110001110001112220001112220102000", "1110001110001110001110001112220001112211222", "0001110001110001110001110001112220002331000", "1110001110001110001110001110001112220300222", "00011100011100011100011100011100011100#0111" }

  38. 29

    26

    28

    Returns: {"00021210101010101010101010101", "11121210101010101010101010101", "00021210101010101010101010101", "11100021210101010101010101010", "00011121210101010101010101010", "11100021210101010101010101010", "00011100021210101010101010101", "11100011121210101010101010101", "00011100021210101010101010101", "11100011100021210101010101010", "00011100011121210101010101010", "11100011100021210101010101010", "00011100011100021210101010101", "11100011100011121210101010101", "00011100011100021210101010101", "11100011100011100021210101010", "00011100011100011121210101010", "11100011100011100021210101010", "00011100011100011100021210101", "11100011100011100011121210101", "00011100011100011100021210101", "11100011100011100011100031010", "00011100011100011100011131010", "11100011100011100011100031010", "00011100011100011100011122333", "11100011100011100011100021100", "0001110001110001110001110130#", "11100011100011100011122202330", "00011100011100011100011102200" }

  39. 37

    4

    0

    Returns: {"1202000111000111000111000111000111000", "1202111000111000111000111000111000111", "1202000111000111000111000111000111000", "0011222000111000111000111000111000111", "#031000111000111000111000111000111000", "0332111000111000111000111000111000111", "0022000111000111000111000111000111000", "1201212000111000111000111000111000111", "1201212111000111000111000111000111000", "1201212000111000111000111000111000111", "0120101212000111000111000111000111000", "0120101212111000111000111000111000111", "0120101212000111000111000111000111000", "1012010101212000111000111000111000111", "1012010101212111000111000111000111000", "1012010101212000111000111000111000111", "0101201010101212000111000111000111000", "0101201010101212111000111000111000111", "0101201010101212000111000111000111000", "1010120101010101212000111000111000111", "1010120101010101212111000111000111000", "1010120101010101212000111000111000111", "0101012010101010101212000111000111000", "0101012010101010101212111000111000111", "0101012010101010101212000111000111000", "1010101201010101010101212000111000111", "1010101201010101010101212111000111000", "1010101201010101010101212000111000111", "0101010120101010101010101212000111000", "0101010120101010101010101212111000111", "0101010120101010101010101212000111000", "1010101012010101010101010101212000111", "1010101012010101010101010101212111000", "1010101012010101010101010101212000111", "0101010101201010101010101010101212000", "0101010101201010101010101010101212111", "0101010101201010101010101010101212000" }

  40. 17

    5

    0

    Returns: {"01013000111000111", "01013111000111000", "01013000111000111", "33322111000111000", "00112000111000111", "#0310111000111000", "03320222111000111", "00220111000111000", "12012023111000111", "12012023000111000", "12012023111000111", "01201201023111000", "01201201023000111", "01201201023111000", "10120120101023111", "10120120101023000", "10120120101023111" }

  41. 26

    25

    0

    Returns: {"01010101010101010101023111", "01010101010101010101023000", "01010101010101010101023111", "10101010101010101023111000", "10101010101010101023000111", "10101010101010101023111000", "01010101010101023111000111", "01010101010101023000111000", "01010101010101023111000111", "10101010101023111000111000", "10101010101023000111000111", "10101010101023111000111000", "01010101023111000111000111", "01010101023000111000111000", "01010101023111000111000111", "10101023111000111000111000", "10101023000111000111000111", "10101023111000111000111000", "01023111000111000111000111", "01023000111000111000111000", "01023111000111000111000111", "22211000111000111000111000", "11001222000111000111000111", "12202000111000111000111000", "00212111000111000111000111", "#0112000111000111000111000" }

  42. 17

    6

    16

    Returns: {"00011100032102010", "11100011132102010", "00011100032102010", "11100022200011333", "00022211122212200", "22211100011102330", "1110001112220130#", "00011100011101100", "11100011100032021", "00011100011132021", "11100011100032021", "00011132021210210", "11100032021210210", "00011132021210210", "11132010210102101", "00032010210102101", "11132010210102101" }

  43. 41

    0

    32

    Returns: {"11100011100011100011100011100020#00111000", "00011100011100011100011100011120030222111", "11100011100011100011100011100021332000222", "00011100011100011100011100011101122111000", "11100011100011100011100011122200333000111", "00011100011100011100011122200021010111000", "11100011100011100011122200011121010222111", "00011100011100011122200011100021010111000", "11100011100011122200011100012102102000111", "00011100011122200011100022212102102111000", "11100011122200011100011100012102102000111", "00011122200011100011100011101010210123000", "11122200011100011100011122201010210123111", "22200011100011100011100011101010210123000", "00011100011100011100011100020102101010121", "11100011100011100011100011120102101010121", "00011100011100011100011100020102101010121", "11100011100011100011100032101021010101010", "00011100011100011100011132101021010101010", "11100011100011100011100032101021010101010", "00011100011100011100032101010210101010101", "11100011100011100011132101010210101010101", "00011100011100011100032101010210101010101", "11100011100011100032101010102101010101010", "00011100011100011132101010102101010101010", "11100011100011100032101010102101010101010", "00011100011100032101010101021010101010101", "11100011100011132101010101021010101010101", "00011100011100032101010101021010101010101", "11100011100032101010101010210101010101010", "00011100011132101010101010210101010101010", "11100011100032101010101010210101010101010", "00011100032101010101010102101010101010101", "11100011132101010101010102101010101010101", "00011100032101010101010102101010101010101", "11100032101010101010101021010101010101010", "00011132101010101010101021010101010101010", "11100032101010101010101021010101010101010", "00032101010101010101010210101010101010101", "11132101010101010101010210101010101010101", "00032101010101010101010210101010101010101" }

  44. 34

    0

    2

    Returns: {"00#0111000111000111000111000111000", "0300222111000111000111000111000111", "2331000222111000111000111000111000", "2211222000222111000111000111000111", "0102000111000222111000111000111000", "0102111000111000222111000111000111", "0102000111000111000222111000111000", "1010123000111000111000222111000111", "1010123111000111000111000222111000", "1010123000111000111000111000222111", "0101010123000111000111000111000222", "0101010123111000111000111000111000", "0101010123000111000111000111000111", "1010101010123000111000111000111000", "1010101010123111000111000111000111", "1010101010123000111000111000111000", "0101010101010123000111000111000111", "0101010101010123111000111000111000", "0101010101010123000111000111000111", "1010101010101010123000111000111000", "1010101010101010123111000111000111", "1010101010101010123000111000111000", "0101010101010101010123000111000111", "0101010101010101010123111000111000", "0101010101010101010123000111000111", "1010101010101010101010123000111000", "1010101010101010101010123111000111", "1010101010101010101010123000111000", "0101010101010101010101010123000111", "0101010101010101010101010123111000", "0101010101010101010101010123000111", "1010101010101010101010101010123000", "1010101010101010101010101010123111", "1010101010101010101010101010123000" }

  45. 40

    39

    19

    Returns: {"0201010101010101010101010101010101012111", "0201010101010101010101010101010101012000", "0201010101010101010101010101010101012111", "1112101010101010101010101010101010121000", "0002101010101010101010101010101010121222", "1112101010101010101010101010101010121000", "0001210101010101010101010101010102000111", "2221210101010101010101010101010102111000", "0001210101010101010101010101010102000111", "1110002010101010101010101010101020111000", "0001112010101010101010101010101020222111", "1110002010101010101010101010101020111000", "0001110201010101010101010101012111000111", "1112220201010101010101010101012000111000", "0001110201010101010101010101012111000111", "1110001112101010101010101010121000111000", "0001110002101010101010101010121222000111", "1110001112101010101010101010121000111000", "0001110001210101010101010102000111000111", "1110002221210101010101010102111000111000", "0001110001210101010101010102000111000111", "1110001110002010101010101020111000111000", "0001110001112010101010101020222111000111", "1110001110002010101010101020111000111000", "0001110001110201010101012111000111000111", "1110001112220201010101012000111000111000", "0001110001110201010101012111000111000111", "1110001110001112101010121000111000111000", "0001110001110002101010121222000111000222", "1110001110001112101010121000111000222111", "0001110001110001210102000111000222111000", "1110001110002221210102111000222111000111", "0001110001110001210102000222111000111000", "2220001110001110002010222111000111000222", "1112220001110001112010111000111000222111", "0001112220001110002010222111000222111000", "1110001112220002221122111000222111000111", "0001110001112220001332000222111000111000", "1110001110001112220030222111000111000111", "0001110001110001110#00111000111000111000" }

  46. 26

    0

    7

    Returns: {"0001110#001000111000111000", "11122200301222000111000111", "22200013321000111000111000", "00022211220111000111000111", "11100033300222111000111000", "00011121021000222111000111", "11100021021222000222111000", "00011121021000111000222111", "11102010102111000111000222", "22202010102000111000111000", "11102010102111000111000111", "00020101021020111000111000", "11120101021020222111000111", "00020101021020111000111000", "12101010102102000111000111", "12101010102102111000111000", "12101010102102000111000111", "01010101010210123000111000", "01010101010210123111000111", "01010101010210123000111000", "10101010101021010123000111", "10101010101021010123111000", "10101010101021010123000111", "01010101010102101010123000", "01010101010102101010123111", "01010101010102101010123000" }

  47. 22

    12

    0

    Returns: {"1010101010101010123000", "1010101010101010123111", "1010101010101010123000", "0101010121020123000111", "0101010121020123111000", "0101010121020123000111", "1010123000111000111000", "1010123111000111000111", "1010123000111000111000", "0102000111000111000111", "0102111000111000111000", "0102000111000111000111", "#011222000111000111000", "0021000222000111000222", "1220222111222000222111", "1100111000111222111000", "0212020123000111000111", "0212020123111000111000", "0212020123000111000111", "1020101010123000111000", "1020101010123111000111", "1020101010123000111000" }

  48. 34

    16

    16

    Returns: {"0003210101010101010101010101020111", "1113210101010101010101010101020222", "0003210101010101010101010101020111", "1110003210101010101010101020111000", "0001113210101010101010101020222111", "1110003210101010101010101020111000", "0001110003210101010101020111000111", "1110001113210101010101020222111000", "0001110003210101010101020111000111", "1110001110003210201020111000111000", "0001110001113210201020222111000111", "1110001110003210201020111000111000", "0001110001110002120111000111000111", "1110001110001112120222111000111000", "0001110001110002120111000111000111", "1110001110002220011000111000111000", "0001110002221110#21222000111000111", "1110001110002221220111222000111000", "0001110001110001100222000111000111", "1110001110001210212000111000111000", "0001110002221210212111000111000111", "1110001110001210212000111000111000", "0001110001210101020123000111000111", "1110002221210101020123111000111000", "0001110001210101020123000111000111", "1110001210101010101010123000111000", "0002221210101010101010123111000111", "1110001210101010101010123000111000", "0001210101010101010101010123000111", "2221210101010101010101010123111000", "0001210101010101010101010123000111", "1210101010101010101010101010123000", "1210101010101010101010101010123111", "1210101010101010101010101010123000" }

  49. 35

    21

    12

    Returns: {"01010101010101010101010101010123000", "01010101010101010101010101010123111", "01010101010101010101010101010123000", "10101010101010101010101010123000111", "10101010101010101010101010123111000", "10101010101010101010101010123000111", "02010101010101010101010123000111000", "02010101010101010101010123111000111", "02010101010101010101010123000111000", "11132010101010101010121000111000111", "00032010101010101010121222000111000", "11132010101010101010121000111000111", "00011132010101010121000111000111000", "11100032010101010121222000111000111", "00011132010101010121000111000111000", "11100011132010121000111000111000111", "00011100032010121222000111000111000", "11100011132010121000111000111000111", "00011100011222000111000111000111000", "11100022210011222000111000111000111", "00011100020221000111000111000111000", "111000111212#0111000111000111000111", "00011100021100222111000111000111222", "11100011102012000222111000111222000", "00011122202012111000222111222000111", "11100011102012000111000222000111000", "00011102010101212000111000111000111", "11122202010101212111000111000111000", "00011102010101212000111000111000111", "11102010101010101212000111000111000", "22202010101010101212111000111000111", "11102010101010101212000111000111000", "02010101010101010101212000111000111", "02010101010101010101212111000111000", "02010101010101010101212000111000111" }

  50. 37

    25

    2

    Returns: {"1010101010101010101010101010101023111", "1010101010101010101010101010101023000", "1010101010101010101010101010101023111", "0101010101010101010101010101023111000", "0101010101010101010101010101023000111", "0101010101010101010101010101023111000", "1010101010101010101010101023111000111", "1010101010101010101010101023000111000", "1010101010101010101010101023111000111", "0101010101010101010101023111000111000", "0101010101010101010101023000111000111", "0101010101010101010101023111000111000", "1010101010101010121023111000111000111", "1010101010101010121023000111000111000", "1010101010101010121023111000111000111", "0101010101020123000111000111000111000", "0101010101020123111000111000111000111", "0101010101020123000111000111000111000", "1020121023111000111000111000111000111", "1020121023000111000111000111000111000", "1020121023111000111000111000111000111", "0212000111000111000111000111000111000", "0212111000111000111000111000111000111", "0212000111000111000111000111000111000", "1100222000111000111000111000111000111", "12#0111222000111000111000111000111000", "0221222000111000111000111000111000111", "0011000111000111000111000111000111000", "1202123000111000111000111000111000111", "1202123111000111000111000111000111000", "1202123000111000111000111000111000111", "0120201212023111000111000111000111000", "0120201212023000111000111000111000111", "0120201212023111000111000111000111000", "1012010101201020123000111000111000111", "1012010101201020123111000111000111000", "1012010101201020123000111000111000111" }

  51. 38

    17

    7

    Returns: {"01010101010101010101201010123000111000", "01010101010101010101201010123111000111", "01010101010101010101201010123000111000", "10101010101010101212020123000111000111", "10101010101010101212020123111000111000", "10101010101010101212020123000111000111", "01010101010201212000111000111000111000", "01010101010201212111000111000111000111", "01010101010201212000111000111000111000", "12102010102123000111000111000111000111", "12102010102123111000111000111000111000", "12102010102123000111000111000111000111", "00011131021000111000111000111000111000", "11100031021222000111000111000111000111", "00011131021000111222111000111222111000", "11100022200111222000222111222000222111", "00022200110222000111000222000111000222", "2221110#212000111000111000111000111000", "00022212202111000111000111000111000111", "11100011002000111000111000111000111000", "00012102123111000111000111000111000111", "22212102123000111000111000111000111000", "00012102123111000111000111000111000111", "11121010201020111000111000111000111000", "00021010201020222111000111000111000111", "11121010201020111000111000111000111000", "02010101010101020123000111000111000111", "02010101010101020123111000111000111000", "02010101010101020123000111000111000111", "10101010101010101010123000111000111000", "10101010101010101010123111000111000111", "10101010101010101010123000111000111000", "01010101010101010101010121020123000111", "01010101010101010101010121020123111000", "01010101010101010101010121020123000111", "10101010101010101010101010101010123000", "10101010101010101010101010101010123111", "10101010101010101010101010101010123000" }

  52. 40

    5

    35

    Returns: {"0001110001110001110001110001110002120121", "1110001110001110001110001110001112120121", "0001110001110001110001110001110002120121", "1110001110001110001110001110002220011000", "0001110001110001110001110002221110221222", "11100011100011100011100011100022212#0111", "0001110001110001110001110001110001100222", "1110001110001110001110001110001110212000", "0001110001110001110001110001112220212111", "1110001110001110001110001110001110212000", "0001110001110001110001110001113201020121", "1110001110001110001110001110003201020121", "0001110001110001110001110001113201020121", "1110001110001110001110001113201010101010", "0001110001110001110001110003201010101010", "1110001110001110001110001113201010101010", "0001110001110001110001113201010101010101", "1110001110001110001110003201010101010101", "0001110001110001110001113201010101010101", "1110001110001110001113201010101010101010", "0001110001110001110003201010101010101010", "1110001110001110001113201010101010101010", "0001110001110001113201010101010101010101", "1110001110001110003201010101010101010101", "0001110001110001113201010101010101010101", "1110001110001113201010101010101010101010", "0001110001110003201010101010101010101010", "1110001110001113201010101010101010101010", "0001110001113201010101010101010101010101", "1110001110003201010101010101010101010101", "0001110001113201010101010101010101010101", "1110001113201010101010101010101010101010", "0001110003201010101010101010101010101010", "1110001113201010101010101010101010101010", "0001113201010101010101010101010101010101", "1110003201010101010101010101010101010101", "0001113201010101010101010101010101010101", "1113201010101010101010101010101010101010", "0003201010101010101010101010101010101010", "1113201010101010101010101010101010101010" }

  53. 41

    16

    34

    Returns: {"00011100011132012101010102101010101010101", "11100011100032012101010102101010101010101", "00011100011132012101010102101010101010101", "11100011100011100032102010210101010101010", "00011100011100011132102010210101010101010", "11100011100011100032102010210101010101010", "00011100011100011100011132021210101010101", "11100011100011100011100032021210101010101", "00011100011100011100011132021210101010101", "11100011100011100011100011100021210101020", "00011100011100011100011100011121210101020", "11100011100011100011100011100021210101020", "00011100011100011100011100011100021020111", "11100011100011100011100011100011121020222", "00011100022200022200022200022200021020111", "11100022211122211122211122211122200112000", "0002221110001110001110001110001110#212111", "22211100011100011100011100011100012202000", "11100011100011100011100011100022211001222", "00011100011100011100011100011100022211000", "11100011100011100011100011100012101023111", "00011100011100011100011100022212101023000", "11100011100011100011100011100012101023111", "00011100011100011100011100032101010101020", "11100011100011100011100011132101010101020", "00011100011100011100011100032101010101020", "11100011100011100011132012101010101010101", "00011100011100011100032012101010101010101", "11100011100011100011132012101010101010101", "00011100011100032102010101010101010101010", "11100011100011132102010101010101010101010", "00011100011100032102010101010101010101010", "11100011132012101010101010101010101010101", "00011100032012101010101010101010101010101", "11100011132012101010101010101010101010101", "00011132010101010101010101010101010101010", "11100032010101010101010101010101010101010", "00011132010101010101010101010101010101010", "11132010101010101010101010101010101010101", "00032010101010101010101010101010101010101", "11132010101010101010101010101010101010101" }

  54. 43

    15

    6

    Returns: {"1010101010101010101010123000111000111000111", "1010101010101010101010123111000111000111000", "1010101010101010101010123000111000111000111", "0101010101010121020123000111000111000111000", "0101010101010121020123111000111000111000111", "0101010101010121020123000111000111000111000", "1010101020123000111000111000111000111000111", "1010101020123111000111000111000111000111000", "1010101020123000111000111000111000111000111", "0201210212000111000111000111000111000111000", "0201210212111000111000111000111000111000111", "0201210212000111000111000111000111000111000", "1110001100222000111000111000111000111000111", "0002221220111222000111000111000111000111000", "2221110021222000111000111000111000111000111", "111000#011000111000111000111000111000111000", "0001112120111000111000111000111000111000111", "1110002120222111000111000111000111000111000", "0001112120111000111000111000111000111000111", "1112020201000111000111000111000111000111000", "0002020201222000111000111000111000111000111", "1112020201000111000111000111000111000111000", "0201201010121023111000111000111000111000111", "0201201010121023000111000111000111000111000", "0201201010121023111000111000111000111000111", "1010120101010101023111000111000111000111000", "1010120101010101023000111000111000111000111", "1010120101010101023111000111000111000111000", "0101012010101010101020121023111000111000111", "0101012010101010101020121023000111000111000", "0101012010101010101020121023111000111000111", "1010101201010101010101010101023111000111000", "1010101201010101010101010101023000111000111", "1010101201010101010101010101023111000111000", "0101010120101010101010101010101023111000111", "0101010120101010101010101010101023000111000", "0101010120101010101010101010101023111000111", "1010101012010101010101010101010101023111000", "1010101012010101010101010101010101023000111", "1010101012010101010101010101010101023111000", "0101010101201010101010101010101010101023111", "0101010101201010101010101010101010101023000", "0101010101201010101010101010101010101023111" }

  55. 44

    11

    25

    Returns: {"00011100011100011121010101021010121000111000", "11100011100011100021010101021010121222000111", "00011100011100011121010101021010121000111000", "11100011100011100012102010102123000111000111", "00011100011100022212102010102123111000111000", "11100011100011100012102010102123000111000111", "00011100011100011100011131021000111000111000", "11100011100011100011100031021222000111000111", "00011100011100011100011131021000111000111000", "11100011100011100011100022200111222111000111", "00011100011100011100022200110222000222111000", "1110001110001110002221110#212000111000222111", "00011100011100011100022212202111000111000222", "11100011100011100011100011002000111000111000", "00011100011100011100012102123111000111000111", "11100011100011100022212102123000111000111000", "00011100011100011100012102123111000111000111", "11100011100011100011121010201020111000111000", "00011100011100011100021010201020222111000111", "11100011100011100011121010201020111000111000", "00011100011100012102010101010101023111000111", "11100011100022212102010101010101023000111000", "00011100011100012102010101010101023111000111", "11100011100011121010101010101010101020111000", "00011100011100021010101010101010101020222111", "11100011100011121010101010101010101020111000", "00011100011102010101010101010101010102000111", "11100011122202010101010101010101010102111000", "00011100011102010101010101010101010102000111", "11100011100020101010101010101010101010121000", "00011100011120101010101010101010101010121222", "11100011100020101010101010101010101010121000", "00011100012101010101010101010101010101012111", "11100022212101010101010101010101010101012000", "00011100012101010101010101010101010101012111", "11100011121010101010101010101010101010101020", "00011100021010101010101010101010101010101020", "11100011121010101010101010101010101010101020", "00011132010101010101010101010101010101010101", "11100032010101010101010101010101010101010101", "00011132010101010101010101010101010101010101", "11132010101010101010101010101010101010101010", "00032010101010101010101010101010101010101010", "11132010101010101010101010101010101010101010" }

  56. 46

    44

    33

    Returns: {"1113201010101010101010101010101010101010101010", "0003201010101010101010101010101010101010101010", "1113201010101010101010101010101010101010101010", "0001113201010101010101010101010101010101010101", "1110003201010101010101010101010101010101010101", "0001113201010101010101010101010101010101010101", "1110001113201010101010101010101010101010101010", "0001110003201010101010101010101010101010101010", "1110001113201010101010101010101010101010101010", "0001110001113201010101010101010101010101010101", "1110001110003201010101010101010101010101010101", "0001110001113201010101010101010101010101010101", "1110001110001113201010101010101010101010101010", "0001110001110003201010101010101010101010101010", "1110001110001113201010101010101010101010101010", "0001110001110001113201010101010101010101010101", "1110001110001110003201010101010101010101010101", "0001110001110001113201010101010101010101010101", "1110001110001110001113201010101010101010101010", "0001110001110001110003201010101010101010101010", "1110001110001110001113201010101010101010101010", "0001110001110001110001112101010101010101010121", "1110001110001110001110002101010101010101010121", "0001110001110001110001112101010101010101010121", "1110001110001110001110001010101010101010123000", "0001110001110001110002221010101010101010123111", "1110001110001110001110001010101010101010123000", "0001110001110001110001110201010101010102000111", "1110001110001110001112220201010101010102111000", "0001110001110001110001110201010101010102000111", "2220001110001110001110001113201010101010111000", "1112220001110001110001110003201010101010222111", "0001112220001110001110001113201010101010111000", "1110001112220001110001110001112101010121000111", "0001110001112220001110001110002101010121222000", "1110001110001112220001110001112101010121000111", "0001110001110001112220001110001010123000111000", "1110001110001110001112220002221010123111000111", "0001110001110001110001112220001010123000111000", "1110001110001110001110001112220123000111000222", "0001110001110001110001110001110123111000222111", "1110001110001110001110001112220123000222111000", "0001110001110001110001110001112200222111000111", "1110001110001110001110001110002330111000111000", "000111000111000111000111000222130#000111000111", "1110001110001110001110001110001100111000111000" }

  57. 47

    41

    32

    Returns: {"00032101010101010101010101012010101010101010101", "11132101010101010101010101012010101010101010101", "00032101010101010101010101012010101010101010101", "11100032101010101010101010101201010101010101010", "00011132101010101010101010101201010101010101010", "11100032101010101010101010101201010101010101010", "00011100032101010101010101010120101010101010101", "11100011132101010101010101010120101010101010101", "00011100032101010101010101010120101010101010101", "11100011100032101010101010101012010101010101010", "00011100011132101010101010101012010101010101010", "11100011100032101010101010101012010101010101010", "00011100011100032101010101010101201010101010101", "11100011100011132101010101010101201010101010101", "00011100011100032101010101010101201010101010101", "11100011100011100032101010101010120101010101010", "00011100011100011132101010101010120101010101010", "11100011100011100032101010101010120101010101010", "00011100011100011100020101010101012010101010121", "11100011100011100011120101010101012010101010121", "00011100011100011100020101010101012010101010121", "11100011100011100011101010101010101201010123000", "00011100011100011122201010101010101201010123111", "11100011100011100011101010101010101201010123000", "00011100011100011100012101010101012010102000111", "11100011100011100022212101010101012010102111000", "00011100011100011100012101010101012010102000111", "11100011100011100011100032101010120101010111000", "00011100011100011100011132101010120101010222111", "11100011100011100011100032101010120101010111000", "00011100011100011100011100020101012020121000111", "11100011100011100011100011120101012020121222000", "00011100011100011100011100020101012020121000111", "11100011100011100011100011101010101212000111000", "00011100011100011100011122201010101212111000111", "11100011100011100011100011101010101212000111000", "00011100011100011100011100012102012000111000222", "11100011100011100011100022212102012111000222111", "00011100011100011100011100012102012000222111000", "11100011100011100011100011100021100222111000111", "00011100011100011100011100011121220111000111000", "11100011100011100011100011100020#21000111000111", "00011100011100011100011100022210011222000111000", "11100011100011100011100011100011222000111000111", "00011100011100011100011100011132010111000111000", "11100011100011100011100011100032010222111000111", "00011100011100011100011100011132010111000111000" }

  58. 4

    1

    1

    Returns: {"0011", "0#21", "3220", "3300" }

    The example output represents the following 4x4 board with five trominoes: 0011 0#21 3220 3300

  59. 7

    1

    5

    Returns: {"1123344", "12235#4", "0066557", "0446877", "1242889", "1232299", "1233000" }

  60. 47

    23

    42

    Returns: {"00011132010101010101010101010101201010101010101", "11100032010101010101010101010101201010101010101", "00011132010101010101010101010101201010101010101", "11100011132012102010101010101010120101010101010", "00011100032012102010101010101010120101010101010", "11100011132012102010101010101010120101010101010", "00011100011100011132010101010101012010101010101", "11100011100011100032010101010101012010101010101", "00011100011100011132010101010101012010101010101", "11100011100011100011132012102010101201010101010", "00011100011100011100032012102010101201010101010", "11100011100011100011132012102010101201010101010", "00011100011100011100011100011132010120201010101", "11100011100011100011100011100032010120201010101", "00011100011100011100011100011132010120201010101", "11100011100011100011100011100011132012120101020", "00011100011100011100011100011100032012120101020", "11100011100011100011100011100011132012120101020", "00011100011100011100011100011100011100012013111", "11100011100011100011100011100011100022212013000", "00011100011100011100011100011100011100012013111", "11122211100011122211100011122211100011100222000", "22200022211122200022211122200022211122201100222", "000111000222000111000222000111000222000212#0111", "11100011100011100011100011100011100011120221222", "00011100011100011100011100011100011100020011000", "11100011100011100011100011100011100011132120121", "00011100011100011100011100011100011100032120121", "11100011100011100011100011100011100011132120121", "00011100011100011100011100011100011132010201010", "11100011100011100011100011100011100032010201010", "00011100011100011100011100011100011132010201010", "11100011100011100011100011132012102010101010101", "00011100011100011100011100032012102010101010101", "11100011100011100011100011132012102010101010101", "00011100011100011100011132010101010101010101010", "11100011100011100011100032010101010101010101010", "00011100011100011100011132010101010101010101010", "11100011100011132012102010101010101010101010101", "00011100011100032012102010101010101010101010101", "11100011100011132012102010101010101010101010101", "00011100011132010101010101010101010101010101010", "11100011100032010101010101010101010101010101010", "00011100011132010101010101010101010101010101010", "11132012102010101010101010101010101010101010101", "00032012102010101010101010101010101010101010101", "11132012102010101010101010101010101010101010101" }

  61. 47

    46

    45

    Returns: {"00021210101010101010101010101010101010101010101", "11121210101010101010101010101010101010101010101", "00021210101010101010101010101010101010101010101", "11100021210101010101010101010101010101010101010", "00011121210101010101010101010101010101010101010", "11100021210101010101010101010101010101010101010", "00011100021210101010101010101010101010101010101", "11100011121210101010101010101010101010101010101", "00011100021210101010101010101010101010101010101", "11100011100021210101010101010101010101010101010", "00011100011121210101010101010101010101010101010", "11100011100021210101010101010101010101010101010", "00011100011100021210101010101010101010101010101", "11100011100011121210101010101010101010101010101", "00011100011100021210101010101010101010101010101", "11100011100011100021210101010101010101010101010", "00011100011100011121210101010101010101010101010", "11100011100011100021210101010101010101010101010", "00011100011100011100021210101010101010101010101", "11100011100011100011121210101010101010101010101", "00011100011100011100021210101010101010101010101", "11100011100011100011100021210101010101010101010", "00011100011100011100011121210101010101010101010", "11100011100011100011100021210101010101010101010", "00011100011100011100011100021210101010101010101", "11100011100011100011100011121210101010101010101", "00011100011100011100011100021210101010101010101", "11100011100011100011100011100021210101010101010", "00011100011100011100011100011121210101010101010", "22200011100011100011100011100021210101010101010", "11122200011100011100011100011100021210101010101", "00011122200011100011100011100011121210101010101", "11100011122200011100011100011100021210101010101", "00011100011122200011100011100011100021210101010", "11100011100011122200011100011100011121210101010", "00011100011100011122200011100011100021210101010", "11100011100011100011122200011100011100021210101", "00011100011100011100011122200011100011121210101", "11100011100011100011100011122200011100021210101", "00011100011100011100011100011122200011100021010", "11100011100011100011100011100011122200011121010", "00011100011100011100011100011100011122200021010", "11100011100011100011100011100011100011122200333", "00011100011100011100011100011100011100011102211", "11100011100011100011100011100011100011100012331", "00011100011100011100011100011100011100022210300", "111000111000111000111000111000111000111000100#0" }

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