The letters A through U represent different natural numbers under 100, in the below triangle:

    
         A
        B C 
       D E F
      G H I J
     K L M N O
    P Q R S T U

Each letter is the sum of the two natural numbers just below it.

What is each letter if C > B?

Made a little Excel spreadsheet for myself (gotta love that sum function!) and after playing around with the bottom row for 20 minutes, I think I finally found a solution. It became clear pretty quickly that the lowest possible numbers should be concentrated at the center of the pyramid, and I had a couple of solutions with A=100, but it took me a while to get that number down to two digits!

98
46, 52
26, 20, 32
17, 9, 11, 21
12, 5, 4, 7, 14
10, 2, 3, 1, 6, 8

Posted by Jyqm on 2011-03-31 11:58:48