## Solution:
The problem of the [last contest](https://www.palnet.io/puzzle/@quantumdeveloper/math-contest-10-1-1-sbi) was:
![Screenshot from 2019-09-17 10-21-44.png](https://cdn.steemitimages.com/DQmW2TjVub5KBAunm3p6tZimKJULAhS2AgWEUu7iZ5HvxCd/Screenshot%20from%202019-09-17%2010-21-44.png)
This is basically a system of 2 equations:
1: `x² + y = 1`
2: `x + y² = 1`
From 1 we can derive:
3: `y = 1-x²`
3 in 2:
`x+(1-x²)² = 1` | -1
`(x-1)+(1-x²)² = 0` → x₁ = 1
`x⁴ - 2x² + 1 + x - 1 = 0`
`x⁴ - 2x² + x = 0` → x₂ = 0
↓
`x³ - 2x + 1 = 0` | ÷(x-1). This can be done because x₁ = 1 is an already known 0
`x² + x - 1 = 0`
→ `x₃₋₄ = -½ ± √(¼ + 1) = -½ ± (√5)/2`
→ x₃ = -½ + (√5)/2; x₄ = -½ - (√5)/2
Using equation 3 that yields the following 4 solutions:
`(1; 0)` `(0; 1)`
`(-½ + (√5)/2; -½ + (√5)/2)`
`(-½ - (√5)/2; -½ - (√5)/2)`

*↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓*
### What is your chance of winning:
`p(You Win) = 1/n`, `n = number of entries`

*↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓*
### List of participants with their entries:
Name | solutions found | comment
 - | - | -
@golddeck |`(0, 1)` `(1, 0)`|
@masoom | all four(with rounding errors) |first complete entry → 1 SBI
@mmunited | Nothing but a few formulas for x and y | Accepted anyway due to low number of complete entries. 

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

Winner draw:
![Screenshot from 2019-09-19 10-32-09.png](https://cdn.steemitimages.com/DQmeTytQPqxGkzE4h5z1VXYySY7wUqmLyGFbDoqZEfLd6tr/Screenshot%20from%202019-09-19%2010-32-09.png)
That makes 1 SBI for @masoom and @golddeck:
![Screenshot from 2019-09-19 10-35-52.png](https://cdn.steemitimages.com/DQmUqWhieFJe81oAnetVZcKa9vUWvE6F95jrFc58HZrzTk7/Screenshot%20from%202019-09-19%2010-35-52.png)

*↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓*
### The next contest starts tomorrow. Don't miss it!