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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.