Thursday, April 11, 2019

Domino Square Puzzle

There are 28 different dominoes in a set.  In the puzzle below, four dominoes from a set are placed in the shape of a square.  This is a "domino square."

We can make a puzzle out of a domino square by trying to arrange it so that we have the same number of "pips" (or dots) along each edge of the square.  It could be any number, it just has to be the same one each side.

Notice that the domino square below almost works -- it has 10 pips along three of the four edges, but the botton edge has only 7 pips.

Can you fix this square by replacing one of the dominoes so that every side has 10 pips?  Remember that the dominoes must all be different.

How many domino squares can you make with a single set of dominoes?

For the solution to this puzzle, click here.

Wednesday, July 12, 2017

Saturday, January 14, 2017

Problem-Solving Techniques

The following is a little preview a wonderful new book about problem-solving.  (See below for more information.)

This problem illustrates James Tanton's Problem Solving Tip #6: Eliminate Wrong Answer Choices

Solution:  Let's figure out the answer by eliminating the ones we know are wrong.  Choice (A) can't be right because then both children would be wrong.  Choice (B) can't be right because Juan would be wrong, and we can eliminate choice (C) because it would mean that Lashana were wrong.  But if we have eliminated (A), (B), and (C), then all we have left is (D).  How could it be right? Choice (D) could be right if there were 3 horses on one side and 4 on the other, so that MUST be true!

Now use what you have learned to solve this harder problem:

The problems and the techniques are from the book Avoid Hard Work! … And Other Encouraging Mathematical Problem-Solving Tips for the Young, the Very Young, and the Young at Heart by Maria Droujkova, James Tanton, and Yelena McManaman.  For more information, see