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 |