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Take the numbers 1, 2, 3, 4 and 5 and imagine them written down in every possible order to give 5 digit numbers. Find the sum of the resulting numbers.

Cube Paths

Stage: 3 Challenge Level: Challenge Level:2 Challenge Level:2

The diagram shows a skeletal view of a 2 by 2 by 2 cube with one route 'down' the cube.

How many routes are there on the surface of the cube from A to B?
(No `backtracking' allowed, i.e. each move must be away from A towards B.)

Cube Paths diagram
The NRICH Project aims to enrich the mathematical experiences of all learners. To support this aim, members of the NRICH team work in a wide range of capacities, including providing professional development for teachers wishing to embed rich mathematical tasks into everyday classroom practice. More information on many of our other activities can be found here.
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