Wednesday, November 28, 2007

A Little Bit of Math

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:
$ Value of
$ Value of
Balance remaining
$50 $50
25 25
10 15
8 7
5 2
2 0
--- ---
$100 $99

When he added up the columns as above, he assumed that he still had $1 in the bank. Was he right?


  1. deposits and withdrawals typically don't post until 18:00.

  2. You can't just total up all the "balance remaining" lines in your checkbook and get the total that you spent. This just is just coincidental that it is so close to the actual value (mostly because you did a pseudo-binary series type pattern -- like how 1+2+4+...+2^n=2^(n+1)-1).

    A good counterexample would be to think about if this bank customer withdrew $1 at a time, 100 times. Then, his "balance remaining" column would look like "$99, $98, $97,...", which, if totaled, is way bigger than $100.

  3. The zero in the column balance remaining signifies that if he had $100 in to begin with, that he took $100 out (which he did). The total of the balance remaining column is in effect, a worthless number.

  4. However, if he always took out half of the money that he had remaining in his account, the two columns should add up to the same number. Thats the only way that i could find where the two columns added to the same number. (but when you get right down to it, the bank wouldn't let you take out ie. 25 Cents...)

  5. You all saw right through it.

  6. 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 column must always equal $100, but is purely coincidence that the total of the right-hand column is close to $100.


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