Each week, the game was repeated with different opponents and the total prize was also accumulating. At the end, the prize for the winner was something like some thousands of dollars. Now, I would like to share with you the resolution of this apparently difficult problem. Indeed, I will show to you that there exists a winning strategy for the starting player. Formally, let us define a configuration as

where i, j, k represent the number of sticks at each row. Note that the swapping of two rows produces an equivalent solution and therefore the supposition that i ≤ j ≤ k is without loss of generality, We will say that a configuration C2 is obtained by C1 if there exists a valid movement (stick removal) from configuration C1 that produces C2. If we denote that movement by m, we will denote this transition by

Now, for a configuration W we say that W is a winning configuration if there exists a movement m from W that produces another configuration L and such that every possible moment m’ from L produces another winning configuration W’. Formally, for every state C we define a binary value w(C) as follows

It suffices to define the two base cases w(0, 0, 0) = true and w(0, 0, 1) = false and the remaining winning configurations can be recovered from these two configurations. This problem can be solved by dynamic programming in a fraction of a second. In the following table, I put the winning configurations W and their respective winning moves m. A move is represented by a pair (r, k) where r is the row index (1, 2 or 3) and k is the number of sticks to remove from it. Note that (3, 5, 7) is a winning configuration and so the starting player has a winning strategy.