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Nim

Start with any number of counters in any number of piles. 2 players take it in turns to remove any number of counters from a single pile. The loser is the player who takes the last counter.

Back to Basics

Find b where 3723(base 10) = 123(base b).

Nim-like Games

A collection of games on the NIM theme

Composite Notions

Age 14 to 16
Challenge Level

A composite number is one that is neither prime nor 1.

Show that 10201 is composite in any base.

Likewise show that 10101 is composite in any base.

Further Reading: Learn About Number Bases by Toni Beardon


The NRICH Project aims to enrich the mathematical experiences of all learners. To support this aim, members of the NRICH team work in a wide range of capacities, including providing professional development for teachers wishing to embed rich mathematical tasks into everyday classroom practice.
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