TopCoder Statistics - Problem Statement

Problem Statement

This time, instead of solving an easy problem with a known solution, you will be in charge in solving an old problem with a solution which was unknown to this date. The old question is whether the egg or the chicken came first. This question has been very difficult to answer over the ages, but a chance has finally come: It is said that a new oracle has appeared which knows everything.

You tried asking the question to the oracle, but the oracle refused to answer, arguing that it has already answered the question to n other people and is tired of answering that question. Not to give up, you decided to interview each of the n people. Of them, eggCount people told you that the answer was "The egg", while the remaining n-eggCount people claimed that the answer was "The chicken". Confused by the results, you asked the oracle a second time. The oracle still refused to answer the question, but instead explained the results: In order to hide the truth to those unworthy, the oracle has intentionally given the wrong answer to exactly lieCount people. On the other hand, also to avoid sharing the secret, exactly liarCount people (not necessarily those that were told the right answer by the oracle) have intentionally given you the opposite answer to the one given to them by the oracle.

You are still suspiscious that the explanation given by the oracle is another lie. Given ints n, eggCount, lieCount and liarCount, find out if scenarios exist such that "The egg" or "The chicken" is the correct answer. If there exist scenarios such that either answer is correct, return "Ambiguous" (quotes for clarity). If only one answer has a possible scenario, return "The egg" or "The chicken" (quotes for clarity) depending on the answer. If neither of the answers has a possible scenario, return "The oracle is a lie".

Definition

Class:: ChickenOracle
Method:: theTruth
Parameters:: int, int, int, int
Returns:: String
Method signature:: String theTruth(int n, int eggCount, int lieCount, int liarCount)
(be sure your method is public)

Constraints

n will be between 1 and 1000000, inclusive.
eggCount, lieCount and liarCount will each be between 0 and n, inclusive.

Examples

10

10

0

0

Returns: "The egg"

In this case, every person has answered correctly.
60

40

0

30

Returns: "The oracle is a lie"

According to the oracle, it has told the correct answer to all 60 people and then 30 of them lied to you. However, it contradicts the fact that 40 people have told you one answer and 20 people have told another one.
60

20

5

25

Returns: "The chicken"
1000

500

250

250

Returns: "Ambiguous"
1

1

1

1

Returns: "The egg"
396517

28344

199491

161224

Returns: "The oracle is a lie"
762085

174382

591906

731022

Returns: "The chicken"
245559

225911

154421

4998

Returns: "The oracle is a lie"
519706

277311

364769

257393

Returns: "The oracle is a lie"
72385

31903

7837

10658

Returns: "The oracle is a lie"
559116

187570

443186

60279

Returns: "The oracle is a lie"
621417

180385

641

450302

Returns: "The oracle is a lie"
498424

25415

45906

448391

Returns: "The egg"
325835

238497

114888

85492

Returns: "The egg"
497223

236730

70808

471449

Returns: "The oracle is a lie"
338919

310645

70422

304279

Returns: "The oracle is a lie"
560054

91058

139916

12375

Returns: "The oracle is a lie"
131781

102924

71553

55554

Returns: "The egg"
756935

331458

620003

751210

Returns: "The oracle is a lie"
298057

282337

59551

196826

Returns: "The oracle is a lie"
348407

128958

128612

125877

Returns: "The egg"
933615

357697

739848

43938

Returns: "The oracle is a lie"
768469

426448

235987

333412

Returns: "The egg"
300410

257594

5989

224034

Returns: "The oracle is a lie"
765658

438802

505627

145878

Returns: "The oracle is a lie"
1

0

0

0

Returns: "The chicken"
1

0

0

1

Returns: "The egg"
1

0

1

0

Returns: "The egg"
1

0

1

1

Returns: "The chicken"
1

1

0

0

Returns: "The egg"
1

1

0

1

Returns: "The chicken"
1

1

1

0

Returns: "The chicken"
1

1

1

1

Returns: "The egg"
962850

19055

64313

85888

Returns: "The oracle is a lie"
862583

486499

301630

493215

Returns: "The chicken"
957641

676883

540997

238519

Returns: "The oracle is a lie"
813451

375748

414019

259012

Returns: "The egg"
945090

793978

512433

54330

Returns: "The oracle is a lie"
835921

339171

513339

776135

Returns: "The oracle is a lie"
965509

361898

778610

858544

Returns: "The oracle is a lie"
849225

184371

641096

611762

Returns: "The oracle is a lie"
802246

37329

473034

165902

Returns: "The oracle is a lie"
969311

361659

296286

208426

Returns: "The oracle is a lie"
819514

421564

230281

54819

Returns: "The oracle is a lie"
925310

874810

775864

411750

Returns: "The oracle is a lie"
811502

533611

171872

75650

Returns: "The oracle is a lie"
916436

817088

178455

579562

Returns: "The oracle is a lie"
951774

929187

897231

57006

Returns: "The chicken"
852037

577253

340259

177278

Returns: "The oracle is a lie"
920552

64517

595740

454457

Returns: "The oracle is a lie"
950051

8270

743079

430550

Returns: "The oracle is a lie"
819775

399440

777548

482922

Returns: "The oracle is a lie"
892059

795464

486421

142293

Returns: "The oracle is a lie"
87

49

44

44

Returns: "The egg"
7

5

4

1

Returns: "The chicken"
97

49

42

57

Returns: "The chicken"
53

26

24

25

Returns: "The egg"
100

52

57

41

Returns: "Ambiguous"
36

25

17

16

Returns: "Ambiguous"
64

37

29

28

Returns: "Ambiguous"
88

48

42

40

Returns: "Ambiguous"
4

1

2

1

Returns: "Ambiguous"
58

27

30

23

Returns: "Ambiguous"
29

17

15

12

Returns: "The chicken"
90

44

44

46

Returns: "Ambiguous"
116434

58220

58285

57939

Returns: "Ambiguous"
244034

122250

121998

122176

Returns: "Ambiguous"
995016

497109

497790

497099

Returns: "Ambiguous"
535929

267649

267975

268246

Returns: "The chicken"
479389

239192

239314

239727

Returns: "The egg"
142582

71453

71321

70944

Returns: "Ambiguous"
632259

316275

315904

315926

Returns: "The egg"
494254

246683

247645

247370

Returns: "Ambiguous"
849338

424843

424517

425628

Returns: "Ambiguous"
91724

46223

45983

45750

Returns: "Ambiguous"
917800

458527

458464

459925

Returns: "Ambiguous"
914513

457351

456571

456982

Returns: "The chicken"
931608

465692

465780

466326

Returns: "Ambiguous"
926724

464301

463897

463006

Returns: "Ambiguous"
921449

460204

459308

460862

Returns: "The chicken"
899919

449839

450367

449254

Returns: "The chicken"
849424

424813

424458

424837

Returns: "Ambiguous"
894545

447647

447092

448149

Returns: "The chicken"
903469

451657

452056

451551

Returns: "The chicken"
998912

499229

498025

499226

Returns: "Ambiguous"
980666

416750

300673

301195

Returns: "Ambiguous"
891946

512498

273483

273821

Returns: "Ambiguous"
982760

417827

301373

301904

Returns: "Ambiguous"
864732

368502

265772

266006

Returns: "Ambiguous"
927095

532371

284804

283940

Returns: "The egg"
950896

913780

19042

18860

Returns: "The egg"
833259

800804

16670

16409

Returns: "The egg"
985823

947734

19414

19401

Returns: "The egg"
943694

906696

18872

18914

Returns: "The egg"
932042

36179

18482

18473

Returns: "The chicken"
909322

26763

17953

900154

Returns: "The egg"
888081

862023

17577

879298

Returns: "The chicken"
981719

28783

19506

972012

Returns: "The egg"
936606

909272

18588

927464

Returns: "The chicken"
851974

25238

17057

843425

Returns: "The egg"
909322

26763

17953

900154

Returns: "The egg"
888081

862023

17577

879298

Returns: "The chicken"
981719

28783

19506

972012

Returns: "The egg"
936606

909272

18588

927464

Returns: "The chicken"
851974

25238

17057

843425

Returns: "The egg"
3

2

2

2

Returns: "The chicken"
10

8

2

3

Returns: "The oracle is a lie"
10

7

4

4

Returns: "The oracle is a lie"
60

23

5

25

Returns: "The oracle is a lie"
60

24

20

5

Returns: "The oracle is a lie"
10

3

8

7

Returns: "The chicken"
6

6

4

4

Returns: "The egg"
999

500

250

250

Returns: "The chicken"
10

7

2

2

Returns: "The oracle is a lie"
6

0

3

2

Returns: "The oracle is a lie"
10

7

8

9

Returns: "The egg"
60

20

5

21

Returns: "The chicken"
1000000

1000000

1000000

1000000

Returns: "The egg"
2

1

1

1

Returns: "The oracle is a lie"
60

22

5

25

Returns: "The chicken"
60

40

40

4

Returns: "The chicken"
12833

3

823

283

Returns: "The oracle is a lie"
10

8

3

2

Returns: "The oracle is a lie"
10

0

10

2

Returns: "The oracle is a lie"
60

20

0

0

Returns: "The oracle is a lie"
6

3

3

1

Returns: "The oracle is a lie"
60

20

6

25

Returns: "The oracle is a lie"
100

96

4

5

Returns: "The oracle is a lie"
60

20

5

23

Returns: "The chicken"
6

3

2

2

Returns: "The oracle is a lie"
5

2

2

1

Returns: "The egg"
5

3

1

2

Returns: "The chicken"
60

30

20

0

Returns: "The oracle is a lie"
1000

345

234

123

Returns: "The chicken"
500

251

250

250

Returns: "The oracle is a lie"
100

90

99

99

Returns: "The oracle is a lie"
10

5

3

4

Returns: "Ambiguous"
100

40

95

35

Returns: "The egg"
100

50

50

2

Returns: "Ambiguous"
100

100

100

100

Returns: "The egg"
501

1

2

1

Returns: "The chicken"
10000

1000

2000

1004

Returns: "The chicken"
1000

501

799

298

Returns: "The chicken"
60

20

7

25

Returns: "The chicken"
4

3

4

4

Returns: "The oracle is a lie"
100

55

50

10

Returns: "The oracle is a lie"
100

90

5

5

Returns: "The egg"
3

1

1

1

Returns: "The egg"
40

25

10

5

Returns: "The egg"
10

10

0

10

Returns: "The chicken"
2

1

2

2

Returns: "The oracle is a lie"
10

0

10

0

Returns: "The egg"
60

4

2

3

Returns: "The oracle is a lie"
5

2

2

2

Returns: "The chicken"
3

1

0

0

Returns: "The oracle is a lie"
10

0

10

10

Returns: "The chicken"
3

2

1

1

Returns: "The chicken"
5

1

4

4

Returns: "The oracle is a lie"
7

5

2

3

Returns: "The chicken"
10

4

2

2

Returns: "The chicken"
2

0

2

0

Returns: "The egg"
80

20

10

5

Returns: "The oracle is a lie"
3

2

0

1

Returns: "The egg"
986

466

967

735

Returns: "The oracle is a lie"
2

1

1

2

Returns: "Ambiguous"
10

3

1

3

Returns: "The oracle is a lie"
5

1

1

1

Returns: "The oracle is a lie"
60

40

5

15

Returns: "The egg"
444136

434320

330890

388736

Returns: "The oracle is a lie"
50

41

10

2

Returns: "The oracle is a lie"
40

20

20

20

Returns: "Ambiguous"
100

30

30

32

Returns: "The chicken"
100

9

10

2

Returns: "The oracle is a lie"
40

12

23

35

Returns: "The chicken"
60

20

5

24

Returns: "The oracle is a lie"
3

1

2

2

Returns: "The egg"
9

5

3

4

Returns: "The chicken"
2

1

0

1

Returns: "Ambiguous"
10

10

10

10

Returns: "The egg"
1000

200

400

400

Returns: "Ambiguous"
10

4

7

4

Returns: "The oracle is a lie"
1000

500

350

300

Returns: "Ambiguous"
4

0

2

4

Returns: "The oracle is a lie"
9170

6554

2308

1848

Returns: "The egg"
4

2

1

3

Returns: "Ambiguous"
100

10

10

2

Returns: "The chicken"
10

8

0

0

Returns: "The oracle is a lie"
60

40

5

25

Returns: "The egg"
60

59

1

1

Returns: "The oracle is a lie"
100

2

75

25

Returns: "The egg"
100

5

3

2

Returns: "The chicken"
60

30

0

30

Returns: "Ambiguous"
10

5

4

3

Returns: "Ambiguous"
5

2

2

3

Returns: "The egg"
60

10

7

13

Returns: "The chicken"
100

10

90

0

Returns: "The egg"
100

100

1

100

Returns: "The oracle is a lie"
6

2

4

2

Returns: "Ambiguous"
10

4

4

2

Returns: "Ambiguous"
14

4

2

4

Returns: "The chicken"
4

1

1

1

Returns: "The oracle is a lie"
60

30

5

30

Returns: "The oracle is a lie"
10

0

1

3

Returns: "The oracle is a lie"
10

10

10

0

Returns: "The chicken"
10

1

3

6

Returns: "The egg"
17

10

8

7

Returns: "The egg"
20

15

2

5

Returns: "The egg"
10

5

3

3

Returns: "The oracle is a lie"
10

3

5

8

Returns: "Ambiguous"
10

6

0

6

Returns: "The chicken"
100000

19

20

13

Returns: "The chicken"
11

10

0

1

Returns: "The egg"
60

38

5

25

Returns: "The egg"
60

20

60

50

Returns: "The oracle is a lie"
8

5

2

2

Returns: "The oracle is a lie"
60

8

6

4

Returns: "The chicken"
6

6

6

6

Returns: "The egg"
1000000

1000000

1

1

Returns: "The egg"
60

60

10

20

Returns: "The oracle is a lie"
100

75

56

23

Returns: "The chicken"
6

4

3

1

Returns: "Ambiguous"
60

20

35

25

Returns: "Ambiguous"
10

3

4

6

Returns: "The oracle is a lie"
10

10

1

1

Returns: "The egg"
60

32

5

25

Returns: "The egg"
10

4

3

2

Returns: "The oracle is a lie"
10

10

7

7

Returns: "The egg"
4

2

2

1

Returns: "The oracle is a lie"
30

20

5

15

Returns: "Ambiguous"
60

40

10

20

Returns: "The egg"
60

40

8

26

Returns: "The egg"
60

20

25

5

Returns: "The chicken"
271

65

239

80

Returns: "The oracle is a lie"
10

2

1

2

Returns: "The oracle is a lie"
6

3

1

3

Returns: "The oracle is a lie"
60

10

50

30

Returns: "The oracle is a lie"
4

0

2

1

Returns: "The oracle is a lie"
16

9

8

4

Returns: "The oracle is a lie"
700

200

400

300

Returns: "Ambiguous"
11

0

4

9

Returns: "The oracle is a lie"
10

6

5

1

Returns: "Ambiguous"
6

5

4

3

Returns: "Ambiguous"
20

8

10

10

Returns: "Ambiguous"
60

20

5

35

Returns: "The egg"
100

10

100

100

Returns: "The oracle is a lie"
4

1

2

3

Returns: "Ambiguous"
50

50

50

50

Returns: "The egg"
10

2

2

2

Returns: "The chicken"
8144

7808

4902

7152

Returns: "The oracle is a lie"
6

5

4

4

Returns: "The oracle is a lie"
4

2

2

2

Returns: "Ambiguous"
1000

600

700

100

Returns: "The chicken"
5

3

4

2

Returns: "The egg"
3282

417

115

491

Returns: "The oracle is a lie"
60

40

40

30

Returns: "Ambiguous"
30

20

6

14

Returns: "Ambiguous"
16

8

2

2

Returns: "The oracle is a lie"
6

3

3

4

Returns: "Ambiguous"
20

8

10

2

Returns: "Ambiguous"
5

2

3

1

Returns: "The chicken"
240

100

120

24

Returns: "Ambiguous"
10

0

6

6

Returns: "The chicken"
2

2

1

1

Returns: "Ambiguous"
8

0

4

2

Returns: "The oracle is a lie"
8

4

3

3

Returns: "Ambiguous"
1000

499

300

300

Returns: "The oracle is a lie"
50

25

26

1

Returns: "Ambiguous"

Statistics

Problem Statement for "ChickenOracle"

Problem Statement

Definition

Constraints

Examples