Imagine you work for a factory that makes egg-shaped ornaments. On the packaging, you need to tell customers how high the eggs can be safely dropped from, without them breaking!

How will you use the extra egg so that you don't need to do so many trials?

Perhaps drop the first egg from the 5th floor and if it breaks, use the second egg to test floors 1 to 4. And if it doesn't break...

Can you come up with a strategy using both eggs to minimise the number of trials you'd have to do in the worst case scenario?

What other interesting mathematical questions can you think of to explore next?

Can you devise the most efficient strategy for finding the highest floor from which you can drop the egg safely?

What if there were more floors?

What if you had more eggs?

Imagine a world where we only had 1p coins. In order to be able to make every amount from 1p to 10p, we'd have to carry 10 coins in our pockets...

To lighten the load, we could choose to have coins of two different denominations.

Charlie wants to have 1p and 2p coins.

Alison would prefer 1p and 4p coins.

1p, 1p, 2p, 2p, 2p, 2p (6coins)

1p, 2p, 2p, 2p, 2p, 2p (6coins)

1p, 1p, 1p, 4p, 4p (5 coins)

Try some other coin values and work out the minimum number of coins that would be needed to make every amount from 1p to 10p.

Which coin denominations would you choose so that you can carry as few coins as possible?

Imagine you now need to carry coins that will allow you to make all amounts from 1p to £1 (£1 = 100p).