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
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
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"
List of participants with their scores and chance of winning, sorted by time of entry:
|Name||solutions found||score||chance of winning|
Winner draw(using a self written program):
Congratulations @tonimontana, you won 1 SBI: