Can you explain how this card trick works?
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?
Given a 2 by 2 by 2 skeletal cube with one route `down' the cube.
How many routes are there from A to B?
Baby is two years old now and drinks milk by the quarter pint, so we have decided to call her GILL. Getting her to recognise her name proved difficult, so we put the letters G, I, L, L on separate building blocks. She loves arranging them, but rarely gets them in the right order. One day she managed to produce every possible four-letter 'word': LILG is one such. How many different four-letter
words did she produce that day?
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.