Place each digit from 1 through 9 in the empty squares of the grid so that the three rows across and the three rows down form correct arithmetic statements. All calculations (which involve only positive integers) should be performed using the correct order of operations.
Solution to the Problem:
I began with the middle column and found that there was only one way in which it would work: 8 / 2 x 1 = 4.
Next, I looked at the middle row (containing the answer 19). The numbers in the first column could be 1, 3, 5, 7, or 9 with the corresponding numbers in the last column: 9, 8, 7, 6, or 5.
Those are the only five ways in which you could get 19:
1 + 2 x 9
3 + 2 x 8
5 + 2 x 7
7 + 2 x 6
9 + 2 x 5
But you can eliminate the equations with 1 and 8.
Then I looked at the column that computes to 69. You need two numbers that multiply together and then add a third number to get 69.
You know from the first 2 steps that one of the factors has to be either 5, 7, or 9.
Since I needed a large number to get within 9 (or less) of 69, I tried 9.
Then everything fell into place.
If 9 had not worked, then I would have tried 7 and then 5.
Correctly solved by:
| 1. James Alarie | Flint, Michigan |
| 2. Rob Miles | Northbrook, Illinois |
| 3. Sreeroopa Sankararaman | Singapore, Singapore |
| 4. Amanda Tan Yi Xuan | Melaka, Malaysia |
| 5. Brijesh Dave | Mumbai City, Maharashtra, India |
| 6. Ivy Joseph | Pune, Maharashtra, India |
| 7. Kelly Stubblefield | Mobile, Alabama |
| 8. Kimberly Howe | Vienna, Virginia |
| 9. Travis Riggs | Strasburg, Virginia |
| 10. Travis Harmon |
Mountain View High School, Mountain View, Wyoming |
| 11. Keaton Hurdsman |
Mountain View High School, Mountain View, Wyoming |
| 12. Jared Parkinson |
Mountain View High School, Mountain View, Wyoming |
| 13. James Riter |
Mountain View High School, Mountain View, Wyoming |