Directions: Using the digits 1 to 9 at most one time each, fill in the boxes to make each equation true.

### Hint

What is the largest possible value that the coefficient of b can be?

### Answer

4 + a = 9

3 * b = 6

c – 7 = 1

a = 5, b = 2, c = 8

Number of Unique Solutions: 16

1: 1 + a = 8, 2b = 6, c – 4 = 5 with a = 7, b = 3, c = 9

2: 1 + a = 8, 2b = 6, c – 5 = 4 with a = 7, b = 3, c = 9

3: 1 + a = 8, 3b = 6, c – 4 = 5 with a = 7, b = 2, c = 9

4: 1 + a = 8, 3b = 6, c – 5 = 4 with a = 7, b = 2, c = 9

5: 4 + a = 9, 2b = 6, c – 1 = 7 with a = 5, b = 3, c = 8

6: 4 + a = 9, 2b = 6, c – 7 = 1 with a = 5, b = 3, c = 8

7: 4 + a = 9, 3b = 6, c – 1 = 7 with a = 5, b = 2, c = 8

8: 4 + a = 9, 3b = 6, c – 7 = 1 with a = 5, b = 2, c = 8

9: 5 + a = 9, 2b = 6, c – 1 = 7 with a = 4, b = 3, c = 8

10: 5 + a = 9, 2b = 6, c – 7 = 1 with a = 4, b = 3, c = 8

11: 5 + a = 9, 3b = 6, c – 1 = 7 with a = 4, b = 2, c = 8

12: 5 + a = 9, 3b = 6, c – 7 = 1 with a = 4, b = 2, c = 8

13: 7 + a = 8, 2b = 6, c – 4 = 5 with a = 1, b = 3, c = 9

14: 7 + a = 8, 2b = 6, c – 5 = 4 with a = 1, b = 3, c = 9

15: 7 + a = 8, 3b = 6, c – 4 = 5 with a = 1, b = 2, c = 9

16: 7 + a = 8, 3b = 6, c – 5 = 4 with a = 1, b = 2, c = 9

Source: Robert Kaplinsky

This answer does not seem to fit the problem (please let me know if I am missing something).

The answer I got was:

4 + a = 9

3 * b = 6

c – 7 = 1

a = 5, b = 2, c = 8

I am using this problem in PD tomorrow, so please let me know if there is an error in my thinking. 🙂

Thanks Barb. I’m not sure how that answer got switched into this problem. I can’t remember what answer I originally got. Your’s definitely works though. Probably others too.

Another student came up with

1+a=8

3b=6

c-4=5

a=7, b=2, c=9

The thought process in this question reminds me of Ken Ken Puzzles. These can be played on-line or you can receive an weekly email with printable puzzles. http://www.kenkenpuzzle.com/teachers/classroom

– I do not work for Ken Ken…just love them.

This actually is easy, you just need to figur out the quotient of all of them in a unique perspective.