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Composite Notions
Age 14 to 16
Challenge Level 
The number 2356 in base 10 can be written
$ 2 \times 10^3 + 3 \times 10^2 + 5 \times 10^1 + 6 \times 10^0 = 2000 + 300 + 50 + 6$
So the number 234561 in base y can be written $2 \times y^5 + 3 \times y^4 + 4\times y^3 + 5 \times y^2 + 6 \times y^1 + 1 \times y^0$
How about factorising?
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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.
