Polydron

This activity investigates how you might make squares and pentominoes from Polydron.

If you had 36 cubes, what different cuboids could you make?

Cereal Packets

How can you put five cereal packets together to make different shapes if you must put them face-to-face?

Move a Match

Move a Match

Take $10$ matchsticks and put them into four piles.

For example, you could have a pile of $1$, two piles of $2$ and a pile of $5$:

Now, the idea is to take one matchstick from each of three of the piles and add it to the fourth.
So, for example, we could take one stick from the two piles of $2$ and one from the pile of $5$ and add them to the pile of $1$. This would give:

So now we have two piles of $1$ and two piles of $4$.
We have gone from piles of $2, 2, 1, 5$ to piles of $1, 1, 4, 4$.

How could you put the $10$ matches in four piles so that when you move one match from three of the piles into the fourth, you end up with exactly the same distribution of matches in four piles as when you started? (In other words, in the case above we would have gone from $2, 2, 1, 5$ to $1, 5, 2, 2,$ for example - although this isn't possible!)

Could you arrange, for example, $14$ matchsticks in such a way as to be able to make it work too?
How about $18$ matches?