2025 SSMO Relay Round 3 Problems/Problem 3

Problem

Let $T = TNYWR.$ The numbers $1$ and $2$ are written on a board. Every second, if the numbers currently on the board are $x$ and $y,$ the number $x+y$ is written, and one of $x$ or $y$ is erased. After a finite number of seconds, the larger number on the board is $\left\lfloor\sqrt{T}\right\rfloor$ . How many possible values can the smaller number take?

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2025 SSMO Relay Round 3 Problems/Problem 3

Problem

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