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# Almost Constant Digits

How many ten-digit numbers are there which contain only the digits $1$, $2$ or $3$, and in which any pair of adjacent digits differs by $1$?

If you liked this problem, here is an NRICH task which challenges you to use similar mathematical ideas.

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Age 11 to 14

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How many ten-digit numbers are there which contain only the digits $1$, $2$ or $3$, and in which any pair of adjacent digits differs by $1$?

If you liked this problem, here is an NRICH task which challenges you to use similar mathematical ideas.

This problem is taken from the UKMT Mathematical Challenges.

You can find more short problems, arranged by curriculum topic, in our short problems collection.

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

Investigate how you can work out what day of the week your birthday will be on next year, and the year after...