2025 SSMO Relay Round 4 Problems/Problem 2
Problem
Let 
Jonathan and Kate are playing a game with 
sticks. On each turn, a player may remove 
or 
sticks. The player who picks up the last stick loses. Kate is first to remove sticks, and both players play optimally. For how many values of in the range ![$\left[T^3,2T^3\right]$](http://latex.artofproblemsolving.com/3/1/1/31124d3f1d2fe3a278328400cfd00e978855ca95.png)
does Kate have a winning strategy?
