August 2018
Problem of the Month

Cross Math Puzzle

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

Send any comments or questions to: David Pleacher