July 2011
Problem of the Month

Safe Deposit Box Problem
The MENSA Puzzle Calendar

My brother's safe deposit box number is made up of four digits in the pattern AABB.

The third digit is the sum of the first two digits.

The two-digit number formed by the middle two digits is the square of the last digit.

What is my brother's safe deposit box number?

My brother's safe deposit box number is 3366.

From the two clues, we can write:

B = 2A.
10A + B = B².

Substituting B = 2A in the second equation, we get:

12A = 4A²

So, A = 0 or A = 3.   But A cannot equal 0 because B would equal 0 and the pattern would be AAAA.

Hence, A = 3 and therefore B = 6.

Correctly solved by:

1. John Funk	Ventura, California
2. James Alarie	Flint, Michigan

Send any comments or questions to: David Pleacher