1. Fill a number from 1-9 only once so that the three numbers are identical _ + _ - _ = _ + _ - _ = _ + _ - _ Where should 1, 2, 3, 4, 5, 6, 7, 8, 9 be placed? Three numbers are identical. Sum of these numbers is multiple of 3

2. Fill a number from 1-9 only once so that the three numbers are identical _ + _ - _ = _ + _ - _ = _ + _ - _ Solve: Choose 3 numbers 1, 2, 3 _ + _ - _ + _ + _ - _ + _ + _ - _ =

3. Fill a number from 1-9 only once so that the three numbers are identical _ + _ - _ = _ + _ - _ = _ + _ - _ Solve: 9 + 8 - 1 + 7 + 6 - 2 + 5 + 4 - 3 = Choose 3 numbers 1, 2, 3 33

4. Fill a number from 1-9 only once so that the three numbers are identical 9 + 8 - 1 + 7 + 6 - 2 + 5 + 4 - 3 =33 _ + _ - _ = _ + _ - _ = _ + _ - _ 11 7, 8 and 9 are separated, otherwise the sum/difference of the numbers could never be 11.

5. Fill a number from 1-9 only once so that the three numbers are identical 9 + 8 - 1 + 7 + 6 - 2 + 5 + 4 - 3 =33 7 + _ - _ = 8 + _ - _ = 9 + _ - _ 11 432 654654 321321 6 – 2 = 4 5 – 3 = 2 4 – 1 = 3

6. Fill a number from 1-9 only once so that the three numbers are identical 9 + 8 - 1 + 7 + 6 - 2 + 5 + 4 - 3 =33 7 + 6 - 2 = 8 + 4 - 1 = 9 + 5 - 3 11 432 654654 321321 6 – 2 = 4 5 – 3 = 2 4 – 1 = 3

7. Fill a number from 1-9 only once so that the three numbers are identical 9 + 8 - 1 + 7 + 6 - 2 + 5 + 4 - 3 =33 7 + 6 - 2 = 8 + 4 - 1 = 9 + 5 - 3 11 432 654654 321321 6 – 2 = 4 5 – 3 = 2 4 – 1 = 3

8. Fill a number from 1-9 only once so that the three numbers are identical _ + _ - _ = _ + _ - _ = _ + _ - _ Determine another sets of numbers: 9 + 8 - 4 + 7 + 3 - 5 + 2 + 1 - 6 = Choose 3 numbers 4, 5, 6 15

9. Fill a number from 1-9 only once so that the three numbers are identical 9 + 8 - 4 + 7 + 3 - 5 + 2 + 1 - 6 =15 _ + _ - 4 = _ + _ - 5 = _ + _ - 6 5 5 5 4, 5 and 6 are separated. 91011

10. Fill a number from 1-9 only once so that the three numbers are identical 9 + 8 - 4 + 7 + 3 - 5 + 2 + 1 - 6 =15 _ + _ - 4 = _ + _ - 5 = _ + _ - 6 5 5 5 91011 1+8 2+7 1+9 2+8 3+7 2+9 3+8

11. Fill a number from 1-9 only once so that the three numbers are identical 9 + 8 - 4 + 7 + 3 - 5 + 2 + 1 - 6 =15 2 + 7 - 4 = _ + _ - 5 = _ + _ - 6 5 5 5 91011 1+8 2+7 1+9 2+8 3+7 2+9 3+8

12. Fill a number from 1-9 only once so that the three numbers are identical 9 + 8 - 4 + 7 + 3 - 5 + 2 + 1 - 6 =15 2 + 7 - 4 = 1 + 9 - 5 = _ + _ - 6 5 5 5 91011 1+8 2+7 1+9 2+8 3+7 2+9 3+8

13. Fill a number from 1-9 only once so that the three numbers are identical 9 + 8 - 4 + 7 + 3 - 5 + 2 + 1 - 6 =15 2 + 7 - 4 = 1 + 9 - 5 = 3 + 8 - 6 5 5 5 91011 1+8 2+7 1+9 2+8 3+7 2+9 3+8

14. Fill a number from 1-9 only once so that the three numbers are identical _ + _ - _ = _ + _ - _ = _ + _ - _ Determine another sets of numbers: 8 + 7 - 3 + 5 + 4 - 6 + 2 + 1 - 9 = Choose 3 numbers 3, 6, 9 9

15. Fill a number from 1-9 only once so that the three numbers are identical 8 + 7 - 3 + 5 + 4 - 6 + 2 + 1 - 9 =9 _ + _ - 3 = _ + _ - 6 = _ + _ - 9 3 3 3 6912

16. Fill a number from 1-9 only once so that the three numbers are identical 9 _ + _ - 3 = _ + _ - 6 = _ + _ - 9 3 3 3 6912 8 + 7 - 3 + 5 + 4 - 6 + 2 + 1 - 9 = 1+5 2+4 1+8 2+7 4+5 4+8 5+7

17. Fill a number from 1-9 only once so that the three numbers are identical 9 2 + 4 - 3 = _ + _ - 6 = _ + _ - 9 3 3 3 6912 8 + 7 - 3 + 5 + 4 - 6 + 2 + 1 - 9 = 1+5 2+4 1+8 2+7 4+5 4+8 5+7

18. Fill a number from 1-9 only once so that the three numbers are identical 9 2 + 4 - 3 = 1 + 8 - 6 = _ + _ - 9 3 3 3 6912 8 + 7 - 3 + 5 + 4 - 6 + 2 + 1 - 9 = 1+5 2+4 1+8 2+7 4+5 4+8 5+7

19. Fill a number from 1-9 only once so that the three numbers are identical 9 2 + 4 - 3 = 1 + 8 - 6 = 5 + 7 - 9 3 3 3 6912 8 + 7 - 3 + 5 + 4 - 6 + 2 + 1 - 9 = 1+5 2+4 1+8 2+7 4+5 4+8 5+7

20. There are multiple solutions to this problem Finding a solution requires formulation of a strategy and reasoning. Determining an answer systematically requires integration of addition, subtractions, multiplication & division.By determining every possible combinations, students would practice mental computations, and indirectly determine whether a number is a multiple of 3.