Math Contest #15 Results and Solution
Solution
The problem of this contest was a solution with basically just 4 trivial integer solutions, but it has a nice plot:
Guessing the 4 trivial solutions isn't so hard:
(0, 0), (0, -1), (1, 0), (1, -1)
To be able to plot it you need to separate y:
x - y = x² + y²
↓
y² + y +x²-x = 0
↓
y = -½ ±√(¼-x²+x)
Now you can either plot it by hand or use any kind of software.
To showcase the graph here the image created by @tonimontana:
A circle.
Actually it's not that surprising, after all the equation is pretty similar to the equation of the unit circle(x² + y² = 1).
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What is your chance of winning:
p(You Win) = 1/n, n = number of entries
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List of participants with their entries:
| Name | solutions found | comment |
|---|---|---|
| @tonimontana | Plot | → 1 SBI |
| @sparkesy43 | (1, -1) | → 1 SBI |
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Winner draw:
not needed
Congratulations @tonimontana and @sparkesy43, you won 1 SBI each!
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