Twenty counters, and you take one, two or three each turn. Take the last and you win. Go first and you can be certain of winning — the trick is what you leave, not what you take.
The answer key prints on a separate page.
Every other challenge sheet here asks about a thing sitting still. This one asks about an OPPONENT who is trying to beat you, and the answer has to work whatever they do. That is a different kind of certainty: not "what is the number" but "what can I guarantee". The winning idea is to always leave a multiple of one more than the most you may take — four, when the most is three — because from a multiple your opponent cannot help but leave you something you can finish.
Grabbing the maximum every turn is what a child reaches for, and it throws the game away on the second move. On a winning pile there is exactly one right first move, and half the piles on the sheet are LOSING ones where no first move helps at all — the honest half, where the answer is that going first cannot win. A search never proves that; the multiples-argument proves it in a line.