Turning the Tables
THE CHALLENGE
This started out as a standard multiplication table for the numbers 2 through 9. Then the rows and columns were all mixed up. Finally, most of the numbers have been removed. Put in all the missing numbers!
EXPLORATION
Make one of these puzzles for someone else. How many numbers can you leave out and still have a puzzle that can be completely solved?
Notes
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THE CHALLENGE
Start with the easiest rows and columns and work your way from there.
- 49 must be 7 x 7, so its row and column must be 7.
- 9 must be 3 x 3, so its row and column must be 3.
- 40 must be 5 x 8. 40 and 72 are in the same column, so 40 must be in column 8 and row 5
- 72 is in column 8, so it is in row 9.
- 20 must be 4 x 5. There is already a row for 5, so 20 must be in row 4 and column 5.
- 36 is in row 4, so it is in column 9.
- 12 is in row 3, so it is in column 4.
With that much information, the remaining numbers go very quickly.
- 48 is 6 x 8 and there is already a column for 8, so 48 must be in column 6 and row 8.
- The only remaining row, the one at the top, must be for 6.
- The only remaining column, the one second from the far right, must be for 2.