### Painting Cubes

Imagine you have six different colours of paint. You paint a cube using a different colour for each of the six faces. How many different cubes can be painted using the same set of six colours?

### Permute It

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.

### Flagging

How many tricolour flags are possible with 5 available colours such that two adjacent stripes must NOT be the same colour. What about 256 colours?

# Bell Ringing

##### Stage: 3 Challenge Level:

We liked the solutions from Jake and Polly of West Flegg Middle School, Great Yarmouth.

NRICH can change to RNICH, RNCIH, RNIHC, NIRCH, NIRHC, NRCIH and NRIHC.
A peal of bells in which the 24 permutations of 4 bells are rung once each is given by
1234
2143
2413
4231
4321
3412
3142
1324
3124
1342
1432
4123
4213
2431
2341
3214
2314
3241
3421
4312
4132
1423
1243
2134
1234

For other solutions see the article Ding Dong Bell .