**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.

## Comments

### 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

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