Nim
Work backwards from the goal: find the positions you want to leave, and the first move follows.
5 minutes · trains Calculate · points only, never money
There is one pile of counters. You and the bot take turns to take 1, 2 or 3 of them, and whoever takes the last counter wins. You play five games, each with a new pile, and you choose who goes first. The bot plays perfectly whenever it can. Can you find the rule that beats it?
- Game
- 1 of 5
- Counters left
- You won
- 0
- Bot won
- 0
Try it yourself
In Nim, each player takes 1, 2 or 3 counters, and whoever takes the last one wins. The pile has 11 and it is your move. How many do you take?
3 questions, a minute or two. Nothing to finish first.
Want more? Practise Calculate.
Read more
- Backward induction Solve the last decision first, then the one before it, until you reach the move you have to make now.
- Count it through Follow a sequence of moves to its end before you start it, counting what each side wins.
- The Calculate course Lessons and practice for the skill this lab trains.