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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.

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Latin Numbers

Let N be a six digit number with distinct digits. Find the number N given that the numbers N, 2N, 3N, 4N, 5N, 6N, when written underneath each other, form a latin square (that is each row and each column contains all six digits).

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Back to Basics

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

Composite Notions

Stage: 4 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

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