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
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