Card Trick 2

Can you explain how this card trick works?

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?

Cube Paths

Given a 2 by 2 by 2 skeletal cube with one route `down' the cube. How many routes are there from A to B?

Cinema Costs

Stage: 3 Short Challenge Level:

Both $£4.20$ and $£7.70$ are multiples of $70p$, so $£C$ must also be a multiple of $70p$. The only multiple of $70p$ between $£90$ and $£96$ which is a whole number of pounds is $£91$.

$7$ children and $8$ adults cost $7\times £4.20+8\times £7.70=£29.40+£61.60=£91$.

Or

$18$ children and $2$ adults cost $18\times £4.20 + 2\times £7.70 = £75.60 + £15.40 = £91$.

This problem is taken from the UKMT Mathematical Challenges.
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