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Difference between revisions of "2025 SSMO Relay Round 1 Problems"
(→‎Problem 2)
 
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==Problem 2==
 
==Problem 2==
  
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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.
+
Let <math>T = TNYWR.</math> A positive integer is called <i>zro</i> 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]]

Latest revision as of 22:04, 21 October 2025

Problem 1

Let $x_1, x_2, \ldots, x_7$ be distinct integers such that the mean of $\{x_i,x_{i+1},x_{i+2}\}$ is an integer for all integers $1\le i\le 5$. Find the minimum possible positive value of $x_7 - x_1$.

Solution

Problem 2

Let $T = TNYWR.$ A positive integer is called zro if more than half of its digits are $0$. Find the sum of the first $T^2$ zro numbers.

Solution

Problem 3

Let $T = TNYWR.$ Positive integers $m$ and $n$ satisfy $m^2-n^2 = T$. What is the least possible value of $m+n$?

Solution

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