ShootingGallery | Topcoder Archive

Problem Statement

You and your friend are at a shooting gallery, and your friend wants to make a bet that he can hit the target within a certain number of shots. You know that each time he takes a shot, there is an accuracy percent probability that he will hit the target. Return the maximal number of shots at which it is advantageous for you to take the bet. A number n is considered advantageous if the probability that your friend will hit the target in n or less shots is less than 50%.

Definition

Class:: ShootingGallery
Method:: profitableBet
Parameters:: int
Returns:: int
Method signature:: int profitableBet(int accuracy)
(be sure your method is public)

Notes

All shots are independent.
Hint: Try to calculate the probability that your friend will NOT hit the target in n or less shots.

Constraints

accuracy will be between 1 and 100, inclusive.

Examples

```
40
```
```
Returns: 1
```
In this case, he will hit the target in one shot with probability 0.4, and in two or less shots with probability 0.64.
```
20
```
```
Returns: 3
```
In one shot - 0.2. In two or less shots - 0.36. In three or less shots - 0.488. In four or less shots - 0.5904.
```
50
```
```
Returns: 0
```
```
1
```
```
Returns: 68
```

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