1. Strategy to solve complex problems
Use a number 1, 2, 3, 4, 5, 6, 7, 8, 9 only
once so that sum of three numbers are
identical in each row, column and
diagonal:

2. Step 1:
Determine what is known:
• Sum of must be the
sum of a three identical numbers.

3. Step 1:
Determine what is known:
• Sum of must be the
sum of a three identical numbers.

4. Step 1:
Determine what is known:
• Sum of must be the
sum of a three identical numbers.

5. Step 1:
Determine what is known:
• Sum of must be the
sum of a three identical numbers.

6. Step 1:
Determine what is known:
• Sum of must be the
sum of a three identical numbers.
= 45

7. Step 1:
Determine what is known:
• Sum of must be the
sum of a three identical numbers.
= 45

8. Step 2:
Sum of three numbers = 15:
= 45
• 7, 8, 9 are separated. Otherwise
7+8 = 15, 7+9 = 16, and 8+9 = 17.

9. 7 + __ + __ = 8 + __ + __ = 9 + __ + __
Step 2:
Sum of three numbers = 15:
7 + __ + __ = 8 + __ + __ = 9 + __ + __ 8 7 6
6+2
5+3
6+1
5+2
4+3
4+2
5+1

10. 7 + __ + __ = 8 + __ + __ = 9 + __ + __
Step 3:
7 + __ + __ = 8 + __ + __ = 9 + __ + __ 8 7 6
6+2
5+3
6+1
5+2
4+3
4+2
5+1
• 7 & 9 add up to 15 in two separate ways.
• 8 adds up to 15 in three separate ways.

11. 7 + __ + __ = 8 + __ + __ = 9 + __ + __
Step 3:
7 + __ + __ = 8 + __ + __ = 9 + __ + __ 8 7 6
6+2
5+3
6+1
5+2
4+3
4+2
5+1
• 8 has a
corner. 8
• 7 & 9 are in
the middle. 9 7

12. 7 + __ + __ = 8 + __ + __ = 9 + __ + __
Step 3:
7 + __ + __ = 8 + __ + __ = 9 + __ + __ 8 7 6
6+2
5+3
6+1
5+2
4+3
4+2
5+1
• 5 is in the
center, as it
adds 3 ways 8 5 9 7

13. 7 + __ + __ = 8 + __ + __ = 9 + __ + __
Step 3:
7 + __ + __ = 8 + __ + __ = 9 + __ + __ 8 7 6
6+2
5+3
6+1
5+2
4+3
4+2
5+1
• 5 is in the
center, as it
adds 3 ways 8 5 9 7

14. 7 + __ + __ = 8 + __ + __ = 9 + __ + __
Step 3:
7 + __ + __ = 8 + __ + __ = 9 + __ + __ 8 7 6
6+2
5+3
6+1
5+2
4+3
4+2
5+1
• 1, 2 and 3
are filled next 8 3 1 5 9 7 2

15. 7 + __ + __ = 8 + __ + __ = 9 + __ + __
Step 3:
7 + __ + __ = 8 + __ + __ = 9 + __ + __ 8 7 6
6+2
5+3
6+1
5+2
4+3
4+2
5+1
• 6 is next 8 3 1 5 9 6 7 2

16. 7 + __ + __ = 8 + __ + __ = 9 + __ + __
Step 3:
7 + __ + __ = 8 + __ + __ = 9 + __ + __ 8 7 6
6+2
5+3
6+1
5+2
4+3
4+2
5+1
• 4 is the last. 8 3 4 1 5 9 6 7 2