**Mismatch Sum Puzzle**

**- 14 May**

A bank customer had £100 in his account. He then made 6 withdrawals, totaling £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 |

**For Solution :**Click Here

Total is correct this is true banking calculation

ReplyDeleteIt could have been worse. Consider he made the six transactions as below:

ReplyDeleteWithdrawal :: Balance Left

1 :: 99

1 :: 98

1 :: 97

1 :: 96

1 :: 95

95:: 0

Now, sum of two columns is: 100 :: 485.

(It is not correct to sum the columns of "Withdrawals" and "Balance Left" and expect them to be equal!)

there is big jhol in this problem:p

ReplyDeleteAdded incorrectly

ReplyDeleteActually here is the general solution to this problem. If you start with an amount Q and make n withdrawals (n > 2) then the Sum of the balances – Q = sigma i=3 to n (i-2) x n(i) – n1. In other words for 5 withdrawals n1 through n5 you can always balance the 2 columns provided the following holds:

ReplyDeleten3 + 2 X n4 + 3 X n5 = n1

For 10 withdrawals from 300 try these numbers:

220,20,10,10,10,10,8,6,4,2