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:
- Setting y to zero and then find a way to make
x⁰ = x^x
This leads to the solutions(0, 0)
and(1, 0)
- 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:
tH
is text contaI
ns 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?
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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 | 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.
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Winner draw(First 2 for the mistery, other 3 for the equation):
That makes 2 SBI for @tonimontana and 3 SBI for @sidekickmatt:
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Hi @quantumdeveloper, as a holder of TULIPS, you have received a small upvote and this important message.
The TULIP Mania Game has now finished - please read this. You must sell your TULIPS during the following 7 days or they will wilt and die.
To stop receiving this messages, please reply to this comment.
Thanks for participating!
Next game will be announced by @Busbecq some days later.
Stop it! I sold them a week ago!