How Do I Solve This Thing?

You are familiar with Sudoku puzzles. For this variation, place the integers 1 – 9 into each row or column such that the following are true: The product of each set of 3 numbers is given at the beginning or ending of each row or column. 336 is the product of this row. 28 is the product of this column.

Each digit appears exactly once in each row. Each digit appears exactly once in each column. Each digit appears exactly once in each 3 x 3 grid.

Thinking about the prime factorization of each product will help in determining the value of each individual square. For instance, the prime factorization of 60 is 2 x 2 x 3 x 5. 2 x 2 x 3 x 5

2 x 3 x 3 2 x 2 x 2 x 2 x 3 x 7

2x2x72x2x7 2x2x2x2x3 2x2x2x2x3 2x3x3x3x5 2x3x3x3x5

2 x 2 x 3 x 5 2 x 3 x 3 2 x 2 x 2 x 2 x 3 x 7 2x2x72x2x7 2x2x2x2x3 2x2x2x2x3 2x3x3x3x5 2x3x3x3x5 Look for the placement of values like 5 and 7 first. 5 7

2 x 2 x 3 x 5 2 x 3 x 3 2 x 2 x 2 x 2 x 3 x 7 2x2x72x2x7 2x2x2x2x3 2x2x2x2x3 2x3x3x3x5 2x3x3x3x5 Think about the location of 1. Look at the prime factorization of 28. Only 4 and 7 are possible so 1 will appear in the first column. Where? 5 1 7

2 x 2 x 3 x 5 2 x 3 x 3 2 x 2 x 2 x 2 x 3 x 7 2x2x72x2x7 2x2x2x2x3 2x2x2x2x3 2x3x3x3x5 2x3x3x3x5 Eight is a good choice to consider next since it takes three 2’s to create its prime factorization

2 x 2 x 3 x 5 2 x 3 x 3 2 x 2 x 2 x 2 x 3 x 7 2x2x72x2x7 2x2x2x2x3 2x2x2x2x3 2x3x3x3x5 2x3x3x3x5 Now there are only 2 factors left in the prime factorization of 336 and one place remaining in that row. What value belongs in that location?

2 x 2 x 3 x 5 2 x 3 x 3 2 x 2 x 2 x 2 x 3 x 7 2x2x72x2x7 2x2x2x2x3 2x2x2x2x3 2x3x3x3x5 2x3x3x3x5 Where do the remaining values of 2, 3, 4, and 9 belong?

Moving forward, find the values in the corner squares first.