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Learning by Doing

Objective: To construct a 4 × 4 magic square with magic constant 68.
Materials Required: Chart paper, coloured paper, sketch pen, scissors, ruler.

Procedure:
• Take 2 square pieces of size 16 cm × 16 cm from the chart paper.

• Draw two 4 × 4 squares one on each square piece.

• Write even numbers from 2 to 32 in an order in the squares and enclose numbers with
identical shapes using sketch pen as shown in Figure 1.
• Take another square and interchange the numbers in identical shapes as in Figure 2.

2 4 6 8 32 4 6 26

10 12 14 16 10 22 20 16

18 20 22 24 18 14 12 24

26 28 30 32 8 28 30 2

Fig. 1 Fig. 2

• Observe that the sum of numbers taken along any row, column, or diagonal in Figure 2

is 68 (magic constant).
• This is a 4 × 4 magic square with magic sum/constant 68.

Application: This method can also be used to construct a 4 × 4 magic square of some other
magic constants, such as 34, 38, 42, 46, and so on, using 16 consecutive natural numbers
with a common difference.

357 Playing With Numbers