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# Strange Bank Account

## You may also like

### Consecutive Numbers

### Pair Sums

### Negative Dice

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Age 11 to 14

Challenge Level

*Stange Bank Account printable sheet*

In Charlie's Bank you are only allowed to **deposit £2** at a time and **withdraw £3** at a time.

Imagine Alison deposits £2, another £2, another £2, another £2 and then finally withdraws £3. She now has an extra £5 in her account.

What other amounts of money is it possible for Alison to change her account balance by?

Charlie's Bank wants to change its rules whilst ensuring that its customers can still change their account balance by any total.

If Alison is only allowed to **deposit £3** at a time and **withdraw £7** at a time, will she be able change her account balance by any total?

Explore some other deposit and withdrawal amounts.

If Alison is allowed to **deposit £x** and **withdraw £y**, what has to be true about x and y to make sure it is possible to change the account balance by any total?

*You might like to play the game Up, Down, Flying Around, and then take a look at Strange Bank Account (part 2).*

*With thanks to Don Steward, whose ideas formed the basis of this problem.*

An investigation involving adding and subtracting sets of consecutive numbers. Lots to find out, lots to explore.

Five numbers added together in pairs produce: 0, 2, 4, 4, 6, 8, 9, 11, 13, 15 What are the five numbers?

If the odd numbers on two dice are made negative, which of the totals cannot be achieved?