### Consecutive Numbers

An investigation involving adding and subtracting sets of consecutive numbers. Lots to find out, lots to explore.

### Calendar Capers

Choose any three by three square of dates on a calendar page...

### Latin Numbers

Can you create a Latin Square from multiples of a six digit number?

# Almost Constant Digits

##### Stage: 3 Short Challenge Level:

The didgits $1$ and $3$ will always be followed by the digit $2$. The digit $2$ can be followed by either $1$ or $3$. Hence the digit $2$ appears exactly five times in a ten digit number, in alternate positions.

If the first digit is $2$, then in each even position we have two choices, $1$ or $3$. This gives $2\times 2\times 2\times 2\times 2 = 32$ possibilities. Otherwise, the second digit is $2$ and in each odd position we have two choices. So again there are $32$ possibilities, making a total of $64$

This problem is taken from the UKMT Mathematical Challenges.
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