44 monkeys have a total of 1407 bananas. No two monkeys have the same number of bananas. Show that there is a monkey that has exactly twice as many bananas as another one.

(In reply to Solution by grouping by Gamer)

In trying to visualise Gamer's list I compiled a table in Excel; it gets very unwieldy, very quickly.


    1               
    0        1        2       3        4
      -----------------------------------
0  |  1      4      16     64       256
2  |  3    12      48    192      768
4  |  5    20      80    320     1280
6  |  7    28    112     448    1792
8  |  9    36    144     576    2304

The numbers at the top and left are seeds for table formula.

For anyone wanting to build and explore this further, the top '1' is in B9. 
This formula:
             =($B$9+$A11)*(2^(2*B$10))
resides in B11.  It is copied/dragged across the table as well as down the table.  I expect that reasonably advanced Excel users will understand this process, and the appropriate cell reference notation.

Edited on November 14, 2006, 7:04 am

Posted by brianjn on 2006-11-14 02:26:00