Perfect Squares

Like most people, you probably know how to fill in a multiplication table even if it looks like this:

 

The numbers that are given on a table can be called clues. The table above has 20 clues. What is the least number of clues that a table could have and still only have one way to fill it out?

 

Although the table above has just nine clues, there is still only one way to complete it. Nine is the fewest number of clues that will still yield a unique solution.  All of those clues would have to be perfect squares: 1, 4, 9, 16, 25, 36, 49, 64, 81, and 100. One of the clues will be missing, but it isn't difficult to figure out where the missing clue should go.  Always find the factors on the outside of the puzzle BEFORE writing down the products on the inside of the puzzle.

The puzzle above is rated difficulty level ONE because you only need to know 10 multiplication facts to find all the factors. If this puzzle is too easy for you, you can try a more difficult puzzle. Levels FOUR, FIVE, or SIX will be much more challenging, even for adults.

This link, Find the Factors 1-10 excel file, will bring up an excel file with puzzles ranging in difficulty from level ONE to level SIX.  You can type the factors directly onto the excel file. You can also cut and paste puzzles you select onto the small or large templates for printing.

An answer key will be posted one week after a puzzle is published.