### 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.

### 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).

### Back to Basics

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

# Composite Notions

##### Stage: 4 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 $2 \times y^5 + 3 \times y^4 + 4\times y^3 + 5 \times y^2 + 6 \times y^1 + 1 \times y^0$