## A Multiplication Based Logic Puzzle

### 331 and Hockey Sticks

• 331 is a prime number.
• Prime factorization: 331 is prime and cannot be factored.
• The exponent of prime number 331 is 1. Adding 1 to that exponent we get (1 + 1) = 2. Therefore 331 has exactly 2 factors.
• Factors of 331: 1, 331
• Factor pairs: 331 = 1 x 331
• 331 has no square factors that allow its square root to be simplified. √331 ≈ 18.193

How do we know that 331 is a prime number? If 331 were not a prime number, then it would be divisible by at least one prime number less than or equal to √331 ≈ 18.193. Since 331 cannot be divided evenly by 2, 3, 5, 7, 11, 13, or 17, we know that 331 is a prime number.

Print the puzzles or type the factors on this excel file:  10 Factors 2014-12-22

Today’s puzzle looks like a hockey stick. Hockey sticks remind me not only of the obvious winter sport, but also of the Twelve Days of Christmas and Pascal’s triangle.

Dimacs.rutgers.edu explains quite nicely how a hockey stick in Pascal’s triangle can give you the total number of gifts received after one day, two days, three days, and so on. Look at the hockey stick in the illustration of Pascal’s triangle from broadbentmaths.com.

If someone gave you one partridge everyday for 12 days, two turtle doves everyday for 11 days, three French hens everyday for 10 days, etc, etc, and etc, then you would receive 364 gifts. (364 is so easy to remember because it is one less than the number of days in a year.)

A Logical Approach to FIND THE FACTORS: Find the column or row with two clues and find their common factor. Write the corresponding factors in the factor column (1st column) and factor row (top row).  Because this is a level three puzzle, you have now written a factor at the top of the factor column. Continue to work from the top of the factor column to the bottom, finding factors and filling in the factor column and the factor row one cell at a time as you go.