The model solution for NERC Finals 2025–2026, Problem B is wrong.

The solution claims an optimal strategy: always use $$$\max(a)$$$ to attack $$$\max(b)$$$ (simulate with max-heaps).

Counterexample:

• a = [3,3,4]
• b = [1,5,6].

If Alice follows the model strategy, she plays $$$4 \to 6$$$, so $$$b$$$ becomes $$$[1,2,5]$$$. Then Bob plays $$$5 \to 4$$$ and destroys Alice's $$$4$$$, leaving $$$a=[3,3]$$$, and Bob can force a win from there.

However, Alice has a winning move: play $$$4 \to 5$$$ first, turning $$$b$$$ into $$$[1,1,6]$$$. From this position Alice can force a win (verified by exhaustive game-tree search).

So always attack $$$\max(b)$$$ with $$$\max(a)$$$ is not optimal for this test.

The proof in the editorial contains the step:

Therefore, if we replace the element being attacked with $$$max(b)$$$ ... we can replace $$$b_j$$$ ​ with $$$max(b)$$$ without worsening the situation.

This replacement is unjustified, and the counterexample above shows it is false.