# Heavy Pockets Imagine a world where we only had 1p coins. In order to guarantee we can make every amount from 1p to 10p, we'd have to carry 10 coins in our pockets!

To lighten the load, we could introduce a second denomination of coin...

Charlie suggests having 1p and 2p coins.

Alison suggests having 1p and 4p coins.

How many 1p and 2p coins would Charlie need to carry, to guarantee he could make any amount between 1p and 10p?

How many 1p and 4p coins would Alison need to carry, to guarantee she could make any amount between 1p and 10p?

Choose some coin denominations of your own.

Which two 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).

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

Once you've explored this, you might like to take a look at Lightening the Load.

### Heavy Pockets

For Charlie, he would need to carry six coins, one 1p coin and five 2p coins. The combinations are as follows:
1p = 1 1p coin
2p = 1 2p coin
3p = 1 2p coin and 1 1p coin
4p = 2 2p coins
5p = 2 2p coins and 1 1p coin
6p = 3 2p coins
7p = 3 2p coins and 1 1p coin
8p = 4 2p coins
9p = 4 2p coins and 1 1p coin
10p = 5 2p coins

For Allison, she would need to carry five coins, 2 4p coins and 3 1p coins:
1p = 1 1p coin
2p = 2 1p coins
3p = 3 1p coins
4p = 1 4p coin
5p = 1 4p coin and 1 1p coin
6p = 1 4p coin and 2 1p coins
7p = 1 4p coin and 3 1p coins
8p = 2 4p coins
9p = 2 4p coins and 1 1p coin
10p = 2 4p coins and 2 1p coins ### What coins would you choose?

Those solutions seem to work. What coin values might you choose if you wanted to make every combination up to a bigger number?