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### Number and algebra

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# Strange Bank Account (part 2)

*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.*

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Age 11 to 14

Challenge Level

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

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

Can Alison change the balance in her account by other amounts in many different ways?

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?