Difference between revisions of "2025 SSMO Relay Round 1 Problems"
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==Problem 1== | ==Problem 1== | ||
| + | Let <math>x_1, x_2, \ldots, x_7</math> be distinct integers such that the mean of <math>\{x_i,x_{i+1},x_{i+2}\}</math> is an integer for all integers <math>1\le i\le 5</math>. Find the minimum possible positive value of <math>x_7 - x_1</math>. | ||
[[2025 SSMO Relay Round 1 Problems/Problem 1|Solution]] | [[2025 SSMO Relay Round 1 Problems/Problem 1|Solution]] | ||
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==Problem 2== | ==Problem 2== | ||
| + | Let <math>T = TNYWR.</math> A positive integer is called \textit{zro} if more than half of its digits are <math>0</math>. Find the sum of the first <math>T^2</math> zro numbers. | ||
[[2025 SSMO Relay Round 1 Problems/Problem 2|Solution]] | [[2025 SSMO Relay Round 1 Problems/Problem 2|Solution]] | ||
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==Problem 3== | ==Problem 3== | ||
| + | Let <math>T = TNYWR.</math> Positive integers <math>m</math> and <math>n</math> satisfy <math>m^2-n^2 = T</math>. What is the least possible value of <math>m+n</math>? | ||
[[2025 SSMO Relay Round 1 Problems/Problem 3|Solution]] | [[2025 SSMO Relay Round 1 Problems/Problem 3|Solution]] | ||
Latest revision as of 11:41, 9 September 2025
Problem 1
Let 
be distinct integers such that the mean of 
is an integer for all integers 
. Find the minimum possible positive value of 
.
Problem 2
Let 
A positive integer is called \textit{zro} if more than half of its digits are 
. Find the sum of the first 
zro numbers.
Problem 3
Let Positive integers 
and 
satisfy 
. What is the least possible value of 
?
