December 2016
Problem of the Month

Sierpinski's Christmas Tree





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


Send any comments or questions to: David Pleacher