Difference between revisions of "2022 SSMO Tiebreaker Round Problems"
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==Problem 1== | ==Problem 1== | ||
| − | For all positive integers <math>n,</math> let <math>S(n)</math> denote the least positive integer <math>x</math> such that <math>n+x</math> is a palindrome. Find the value of <math> | + | For all positive integers <math>n,</math> let <math>S(n)</math> denote the least positive integer <math>x</math> such that <math>n+x</math> is a palindrome. Find the value of <math>{\sum_{n=1}^{100}S(n)}.</math> |
[[2022 SSMO Tiebreaker Round Problems/Problem 1|Solution]] | [[2022 SSMO Tiebreaker Round Problems/Problem 1|Solution]] | ||
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==Problem 2== | ==Problem 2== | ||
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[[2022 SSMO Tiebreaker Round Problems/Problem 2|Solution]] | [[2022 SSMO Tiebreaker Round Problems/Problem 2|Solution]] | ||
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==Problem 3== | ==Problem 3== | ||
Latest revision as of 15:22, 2 May 2025
Problem 1
For all positive integers 
let 
denote the least positive integer 
such that 
is a palindrome. Find the value of 
Problem 2
Let 
. If 
where 
are real numbers, then the value of 
can be expressed as 
for relatively prime positive integers 
and 
. Find 
.
Problem 3
Find the sum of the 5 smallest positive prime numbers 
such that 
has no positive integer solutions for .
