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**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:

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

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

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

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

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

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

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

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**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

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**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.

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**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

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**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

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**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

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**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

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**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

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**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

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