The taking game
12 matches lie in a pile on the table. Two players take turns, and on your turn you take between 1 and 2 of them. Whoever takes the very last match wins. You go first.
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. What matters is what you leave, not what you take.
- Try small piles first. 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.
- 12 is already a multiple of 3 — 12 ÷ 3 = 4 whole groups. Whatever you take first, your opponent completes the group and hands a multiple 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 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. What matters is what you leave, not what you take.
- 02
Try small piles first. 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.
- 03
12 is already a multiple of 3 — 12 ÷ 3 = 4 whole groups. Whatever you take first, your opponent completes the group and hands a multiple 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 answer is SECOND.