2025 SSMO Relay Round 1 Problems

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 \textit{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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2025 SSMO Relay Round 1 Problems

Problem 1

Problem 2

Problem 3