### Consecutive Numbers

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

### Pair Sums

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

### Negative Dice

Weekly Problem 16 - 2012
If the odd numbers on two dice are made negative, which of the totals cannot be achieved?

# Strange Bank Account

##### Stage: 3 Challenge Level:

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.