The taking game, step by step
Twenty counters, and you take one, two or three each turn.
Can you be sure to win? If so, how many should you take on your first turn? Write SECOND if going first cannot win.
Sometimes going first is the losing seat
- 12 matches, and each turn takes 1 up to 2. Whoever takes the last one wins, and you go first. Grabbing a lot looks tempting and is exactly how these are lost — the move that matters is what you LEAVE, not what you take.
- Play the tiny piles by hand. A pile of 3 loses for whoever must move: they take between 1 and 2, and you take the rest of the 3, so you win. The same is true of 6, 9, and every multiple of 3 — hand your opponent one of those and they cannot escape it.
- 12 is already a multiple of 3 — 12 ÷ 3 = 4 whole groups. That is the trap, and this time you are the one sitting in it: whatever you take first, your opponent completes the group and hands the multiple straight back.
- You face a multiple of 3 every single turn, so it is your opponent who takes the last one. Going first cannot win here — the honest answer is SECOND.
How it works.
- 01
12 matches, and each turn takes 1 up to 2. Whoever takes the last one wins, and you go first. Grabbing a lot looks tempting and is exactly how these are lost — the move that matters is what you LEAVE, not what you take.
- 02
Play the tiny piles by hand. A pile of 3 loses for whoever must move: they take between 1 and 2, and you take the rest of the 3, so you win. The same is true of 6, 9, and every multiple of 3 — hand your opponent one of those and they cannot escape it.
- 03
12 is already a multiple of 3 — 12 ÷ 3 = 4 whole groups. That is the trap, and this time you are the one sitting in it: whatever you take first, your opponent completes the group and hands the multiple straight back.
- 04
You face a multiple of 3 every single turn, so it is your opponent who takes the last one. Going first cannot win here — the honest answer is SECOND.