Question

Find the magic sum of a magic square of order 6
formed by multiplying each entry of a 6 x 6 normal
magic square with 3.​

Answer 1

Answer:

magic square is an arrangement like the one below where the vertical, horizontal and diagonal lines of numbers all add up to the same value. This ‘same value’ is called the sum of the magic square.

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It’s a critical part of this problem that three times the centre square is equal to the sum of the magic square.

Magic squares are interesting objects in both mathematics proper and in recreational mathematics. It is likely that students have already encountered magic squares. The problems in this sequence give students the opportunity to use known numerical or algebraic concepts.

This problem is part of a series exploring magic squares.  Little Magic Squares  and A Square of Circles , Level 2,  Big Magic Squares  Level 3. Also at Level 4, Negative Magic Squares, . The Magic Square, Level 5 shows why three times the centre number is equal to the sum of the magic square.  Difference Magic Squares at Level 6, looks at an interesting variation of the magic square concept.

Required Resource Materials

Copymaster of the problem (Mā�ori)

Copymaster of the problem (English)

Activity

The Problem

Tui is getting the idea of magic squares. She decides to make all of the magic squares that she can using the fractions 7/6, 4/3, and 3/2.

How many can she make?

It takes her quite a while because she doesn’t know that the sum of a magic square is always three times the number in the centre.

Teaching sequence