Copyright © University of Cambridge. All rights reserved.

See all short problems arranged by curriculum topic in the short problems collection

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.*