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Mismatch Sum Puzzle

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:




WithdrawalsBalance left
£50£50
£25£25
£10£15
£8£7
£5£2
£2£0


£100£99


Why are the Totals not exactly right ?

For Solution : Click Here

5 comments:

  1. Total is correct this is true banking calculation

    ReplyDelete
  2. It could have been worse. Consider he made the six transactions as below:

    Withdrawal :: 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!)

    ReplyDelete
  3. there is big jhol in this problem:p

    ReplyDelete
  4. Added incorrectly

    ReplyDelete
  5. Actually 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:

    n3 + 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

    ReplyDelete