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## 'Strange Bank Account (part 2)' printed from http://nrich.maths.org/

*This problem follows on from Strange Bank Account*.

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

**cancel transactions**.
**Alison found a way of increasing her account balance by £5:**
Seven deposits and three withdrawals:

(+£2) + (+£2) + (+£2) + (+£2) + (+£2) + (+£2) + (+£2) + (-£3) + (-£3) + (-£3)

which Alison wrote as $7\times (+£2) + 3 \times (-£3)$
She then found another way:

One deposit and

**cancelling** one withdrawal, which Alison wrote as $(+£2) - (-£3)$

**Are there other ways in which Alison can ****increase the amount of money in her account by £5? ****How many ways?**
Can Alison change the balance in her account by other amounts in many different ways?

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