## Solution:

The problem of the last contest was:

The best way to reach the 3 solutions was by thinking about how to eliminate the problem that the y in the exponents brings.

One way to do this was using `y = 1`

which simplifies the equation to:`x = x`

So the first solution is `(x, 1)`

.

An other way to eliminate y is to set `x = 0`

. That way both sides become zero, if y is bigger than 0(0⁰ is undefined, 1/0 is infinity).

So the second solution is `(0, y); y > 0`

.

The last solution, which in my opinion is the most intuitive one can be reached by assuming `x = y`

:`x^x = x*x`

`x^x = x²`

|log_x()`x = 2`

So the last solution is `(2, 2)`

*↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓*

### How your chance of winning is calculated:

- Every participant gets 1 point for entering the contest.
- Every solution entered gets 1 additional point.
- Your winning chance is
`"your points"/"total points"`

*↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓*

### List of participants with their scores and chance of winning, sorted by time of entry:

Name | solutions found | score | chance of winning |
---|---|---|---|

@heraclio | `(2, 2)` |
2 | 16.67 % |

@tonimontana | `(x, 1)` , `(2, 2)` , `(0, y), y > 0` |
4 | 33.33 % |

@sidekickmatt | `(2, 1)` , `(2, 2)` , `(0, 1)` , `…` |
4 | 33.33 % |

@vote-transfer | `(2, 2)` |
2 | 16.67 % |

*↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓*

### Winner draw(using a self written program):

Congratulations @tonimontana, you won 1 SBI:

*↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓*

## Comments 1

Damn I got lucky there :)