Math contest #9 Results and Solution

Solution:

The problem of the last contest was:

To find the solutions for this equation you need to think of ways to make both sides equal.
This can be done by:

1. Setting y to zero and then find a way to make x⁰ = x^x
   This leads to the solutions (0, 0) and (1, 0)
2. Assume y = z*x to make the equation simpler:
   x^(zx) = ((z+1)*x)^x
   → x^z = (z+1)*x
   This leads to the solutions (2, 6), (-2, -6), (3, 6) and (-1, 2)

Mystery solution

The last contest also contained a secret message.
This message was encoded in the capital letters, similar to this:
tHis text contaIns a message → HI
Using that method I hid the following message in the contest:
CONGRATULATIONSYOUFOUNDITANDNOWTELLMEWHATYOUTHINKABOUTTHEMYSTERYDOYOUWANTMOREPROBLEMSLIKETHIS
Which is with a bit formatting:
Congratulations, you found it. And now tell me what you think about "The Mystery". Dou you want more problems like this?
↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓

What is your chance of winning:

p(You Win) = 1/n, n = number of entries

↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓

List of participants with their entries:

Name	solutions found	hidden message
@tonimontana	(2, 6), (-2, -6), (3, 6), (0, 0)	GOODSECRET
@sidekickmatt	(1, 0), (-1, 2)	SURE

Based on your responds to the message I will make similar problems in the future.

↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓

Winner draw(First 2 for the mistery, other 3 for the equation):

That makes 2 SBI for @tonimontana and 3 SBI for @sidekickmatt:

↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓

The next contest starts in 2 days. Don't miss it!