How do you set up Nim?

Agree on the rule set first (normal play — last object wins; or misère — last object loses, the traditional default). Then arrange identical objects (coins, matchsticks, pebbles, counters) into piles. The two most popular layouts are the Marienbad / 1-3-5-7 staircase (16 objects in four rows of 1, 3, 5, and 7) and the classic three-pile 3-4-5 (12 objects). Decide who goes first, confirm the pile counts together, and you're ready to play.

What is the difference between normal play and misère Nim?

In normal play , the player who removes the very last object wins . In misère play , the player forced to take the last object loses — meaning you want to leave exactly one object for your opponent. Misère is the traditional version (and the one in the 1961 film Last Year at Marienbad ); normal play is the version analysed in modern combinatorial game theory because the strategy is cleaner. The two rule sets diverge at the move that creates the all-singletons position: in normal play, win by leaving an even number of singleton piles; in misère, leave an odd number.

What age can kids learn Nim?

Nim is suitable for ages 7 and up . The rules — pick one pile, take at least one object, last object wins or loses — are simple enough for early-elementary players to grasp in a couple of minutes. The underlying strategy (binary XOR / nim-sum) is rich enough that the same game engages adults and math students for years. A typical game runs 5 to 15 minutes, making it a great rainy-day or classroom logic/strategy exercise.

Free Printable Nim Rules — How to Play

Q: What is the winning strategy for Nim?

Bouton's theorem (1901): compute the nim-sum — the XOR of all pile sizes in binary. If the nim-sum is non-zero, the player to move has a winning strategy and should play a move that makes the nim-sum zero. If it is already zero, the player to move loses against perfect play. The 1-3-5-7 Marienbad layout has nim-sum zero (1 XOR 3 XOR 5 XOR 7 = 0), so the second player always wins under perfect play. The 3-4-5 layout has nim-sum 2 (non-zero), so the first player always wins.

Q: Can you take from more than one pile in a turn?

No. Every move must come from a single pile . Taking, for example, 2 objects from Row A and 1 object from Row B in the same turn is illegal — that counts as two moves, not one. You also cannot skip your turn (at least one object must be removed) and you cannot split a pile into two smaller piles (a pile of 7 with 3 removed becomes a single pile of 4).

About Free Printable Nim Rules

It depends on which version you agree on before starting. In normal play taking the last object wins; in misère play, the traditional version shown in the 1961 film Last Year at Marienbad, the player forced to take the last object loses.

By the ToolFluency team · Updated October 2026

Want to play instead? Play Nim online, free in your browser. Nim is a 2-player strategy game played with a handful of identical objects such as coins, matchsticks or counters, set out in piles. Players take turns removing any number of objects from one pile, and depending on the version you agree on, taking the last object either wins (normal play) or loses (misère play). A game takes about 5 to 15 minutes, and the full printable rules sheet with pile diagrams is on this page.

How to play Nim

Agree on the win rule: in normal play the player who takes the last object wins; in misère play, the traditional version, the player forced to take the last object loses.
Set out the piles: use 16 objects in four rows of 1, 3, 5 and 7 (the Marienbad layout), or 12 objects in three piles of 3, 4 and 5. Keep the piles clearly apart and agree on the counts before the first move.
Choose who starts: flip a coin, let the youngest go first, or alternate between games.
Take a turn: pick exactly one pile and remove at least one object from it. You may take as many as you like from that pile, up to the whole pile.
Know what's not allowed: you can't take from two piles in one turn, you can't pass, and you can't split a pile into two. A pile of 7 with 3 removed is simply a pile of 4.
Alternate turns until every object has been removed, setting removed objects aside out of play.
Declare the winner: in normal play, whoever took the last object wins; in misère, whoever took it loses. Nim has no ties.

Examples

Strategy tips

Write each pile size in binary and combine them with XOR (the nim-sum). If it is not zero, there is a move that makes it zero, and making it is the winning move.
If the nim-sum is already zero on your turn, you are losing against perfect play. Make a small move and hope your opponent slips.
The 1-3-5-7 layout starts at nim-sum 0, so the second player can always win. In casual games, let the younger or weaker player choose whether to go first or second.
The 3-4-5 layout has nim-sum 2, so the first player can win by taking 2 from the pile of 3, leaving 1-4-5.
In misère play, follow the same nim-sum strategy until only one pile has 2 or more objects. Then take from that pile so you leave an odd number of single-object piles (in normal play, leave an even number).
In normal play, two equal piles are a win for the player who just made them equal: copy whatever your opponent takes from one pile by taking the same from the other.

Example: working out the nim-sum

Start from piles of 3, 4 and 5. In binary these are 011, 100 and 101. XOR them column by column: 011 XOR 100 = 111, and 111 XOR 101 = 010, which is 2. The nim-sum is not zero, so the first player can win. Taking 2 from the pile of 3 leaves 1, 4 and 5 (001, 100, 101), whose nim-sum is 0, handing your opponent a losing position.

Frequently asked questions

Does the player who takes the last object win or lose in Nim?

It depends on which version you agree on before starting. In normal play taking the last object wins; in misère play, the traditional version shown in the 1961 film Last Year at Marienbad, the player forced to take the last object loses.

Can you take from more than one pile in a turn?

No. Every move must come from a single pile. Taking 2 from one row and 1 from another in the same turn counts as two moves and is illegal.

Can you pass or split a pile in Nim?

Neither is allowed. You must remove at least one object every turn, and removing objects never splits a pile into two. A pile of 7 with 3 taken out from the middle is still one pile of 4.

What is the winning strategy for Nim?

Compute the nim-sum, the XOR of all pile sizes in binary (Bouton's theorem, 1901). If it is not zero, the player to move can win by making a move that brings it to zero. If it is already zero, the player to move loses against perfect play.

Who wins 1-3-5-7 Nim with perfect play?

The second player. Its nim-sum is 1 XOR 3 XOR 5 XOR 7 = 0, so whoever moves first is already in a losing position if the other player never makes a mistake.

How is misère strategy different from normal play?

The two only differ near the end. Play the usual nim-sum strategy until exactly one pile has 2 or more objects left. Then, in misère, reduce that pile so your opponent faces an odd number of single-object piles; in normal play, leave an even number.

What is the 21 Game?

It is a single-pile version of Nim with 21 objects, or counting aloud from 1 to 21. Each turn you take 1, 2 or 3, and the player forced to take the 21st (last) object loses. It needs no materials at all.

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You might also need

◎Play Nim Online ◎Dots and Boxes Rules ◎Mancala Rules ◎Reversi Rules ◎Hangman Rules

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