The 111th day of the year for 2012 was April 20th. An interesting way to use the number 111 is to force it with a forcing matrix. Although a forcing matrix is not a commonly known item, it does offer exercises in basic arithmetic. The first source that comes to mind about a forcing matrix comes from Martin Gardner’s Hexaflexagons and Other Mathematical Diversions. However, Doug Dyment has a similar version posted online here. The basic idea for the 111 forcing matrix is to draw out and label a 6 x 6 matrix using the numbers in order, left to right, top to bottom. Take any number and circle it… in this example, circle the number 8. After the number is circled, cross out the remaining numbers in the same row and column as 8. Repeat this process until the matrix is exhausted. Pictured below is the first step followed by an example of what a completed matrix would look like.

The end result should have a total of six numbers circled with the rest crossed out. In this example, the numbers 4, 8, 17, 19, 27, and 36 have been chosen. When the numbers are totaled up, the sum is 111. No matter which numbers are chosen, for this matrix, the total will always equal 111.

References:

D. Dyment, How to construct a forcing matrix from Deceptionary http://www.deceptionary.com/aboutmatrices.html Accessed 20 April 2012

Gardner, M. (1988). Hexaflexagons and other mathematical diversions: The first scientific american book of puzzles and games. Chicago: The University of Chicago Press