Answer to March 2009 Problem of the Month

Can you rank the college logos from the equations below?
Each logo has a value from 1 to 5, and no two logos have the same value.

Give the answer for each of the following logos:

	Wyoming Cowboys =
	Wake Forest Demon Deacons =
	Texas Longhorns =
	Clemson Tigers =
	Colorado State Rams =

Solution to the Problem:

	Wyoming Cowboys = 3
	Wake Forest Demon Deacons = 1
	Texas Longhorns = 5
	Clemson Tigers = 2
	Colorado State Rams = 4

Let A = Demon Deacon
Let B = Tiger Paw
Let C = Cowboy
Let D = Longhorn
Let E = Ram

Then you can write five equations:

A + A = B
A + B = C
C + B = D
E + A = D
B + B = E

There are several ways to solve this.

(1) From the first two equations, you can get C = 3A.

Since all five letters must be in the range from 1 to 5,

A must equal 1 (anything larger forces C to be greater than 5).

Hence, C = 3.

Then, since B = 2A, B equals 2.

Then E = 4 and D = 5.

(2) Since B = 2A and E = 2B,
then E = 4A.

This forces A to be 1 and the rest follows.

Correctly solved by:

1. K. Sengupta	Calcutta, INDIA
2. Jacob Harmon	Mountain View High School, Mountain View, Wyoming
3. Jeremy Harmon	Mountain View High School, Mountain View, Wyoming
4. Halie Gardner	Mountain View High School, Mountain View, Wyoming
5. Isabelle Patnode	John Handley High School, Winchester, Virginia
6. Courtney Feathers	John Handley High School, Winchester, Virginia
7. Meagan Leonard	John Handley High School, Winchester, Virginia
8. Aubrey Wilkerson	John Handley High School, Winchester, Virginia
9. Ben Clarke	John Handley High School, Winchester, Virginia
10. Richard K. Johnson	La Jolla, California
11. Emily Stapp	Mountain View High School, Mountain View, Wyoming
12. Michelle Johnson	Mountain View High School, Mountain View, Wyoming
13. Shay Murray	Mountain View High School, Mountain View, Wyoming
14. Mark O. Kampman	Mountain View High School, Mountain View, Wyoming