Mismatch Sum Puzzle Solution - 14 May
A bank customer had £100 in his account. He then made 6 withdrawals, totalling £100. He kept a record of these withdrawals, and the balance remaining in the account, as follows:
| Withdrawals | Balance left |
|---|
| £50 | £50 |
| £25 | £25 |
| £10 | £15 |
| £8 | £7 |
| £5 | £2 |
| £2 | £0 |
|
|
| £100 | £99 |
Why are the Totals not exactly right ?
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Solution
There is
no reason whatever why the customer's original deposit of £100 should equal the total of the balances left after each withdrawal.
The total of withdrawals in the left-hand colum may equal £100, but is is purely
coincidence that the total of the right-hand column is close to £100.
Let us show another example, but starting with £200 in the bank:
| Withdrawals | Balance left |
| £50 | £150 |
| £25 | £125 |
| £10 | £115 |
| £8 | £107 |
| £5 | £102 |
| £2 | £100 |
|
|
| £100 | £699 |
Moral of this story?
Don't Total Balances.