Mathematical SBI contest #4 Results and Solution of the Equation

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)

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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"

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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 %

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Winner draw(using a self written program):

Congratulations @tonimontana, you won 1 SBI:

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The next contest starts tomorrow. Don't miss it!