Mathematics Problem Of the Week

Spring 2006

POW #3

Pixel Primes

Below are the “pixel prints” of the single digit prime numbers. That is, in a 3x5 grid of pixels, the indicated pixels are lit up to display each of the prime numbers. The problem is to arrange these pixel prints in a way to maximize the value of shared pixels sides. That is, each prime scores its own value times the number of pixel edges it shares with another prime.

For example, just combining 2 and 3, the configuration to the left would yield 2*3 = 6 for the “two” and 3*3 = 9 for the “three” or a total of 15 points.

The configuration to the right has 8 edges shared between the two numbers for a total score of 40 points (2 * 8 + 3 * 8).

You may use each prime only once and while they can be rotated, they cannot be reflected, flipped over or overlapped. The final configuration must lie in one plane. High score wins the prize.

Due Friday, February 17^th Noon

Solutions should be submitted to Dr. R. Lock's mailbox in the Math office or sent via e-mail to rlock@stlawu.edu.