Can you insert the numbers 1, 2, 3, 4, 5, 6, 7, 8, and 9 for the
letters A, B, C, J, K, L, W, X, and Y so that the following statements
are true in the Sierpinski's Christmas Tree below?

          A + B + C = J + K + L = W + X + Y
          A < B < C
          J < K < L
          W < X < Y
          A < J < W



You must send in all solutions in order to get credit.


Solution to the Problem:





First, determine the sum of 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9.
The sum is 45, so each trio of numbers must add up to 15.
There are two ways that this can occur:

1 - 6 - 8,     2 - 4 - 9,     3 - 5 - 7

        and

1 - 5 - 9,     2 - 6 - 7     3 - 4 - 8

Now using the inequalities that were given, you get the two answers above.

Here are the values of each letter:
A=1 B=5 C=9 J=2 K=6 L=7 W=3 X=4 Y=8
A=1 B=6 C=8 J=2 K=4 L=9 W=3 X=5 Y=7


Correctly solved by:

1. James Alarie Flint, Michigan
2. Kimberly Howe Vienna, Virginia
3. Eliza Sheffield Tuscaloosa, Alabama
4. Adalene Thomas Mountain View High School,
Mountain View, Wyoming