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2 years ago

Prepare a grid with magic number 30. You can choose any set of numbers in sequence but the numbers should not be repeated.

Mathematics

1 answer:

Bess [88]2 years ago

5 0

The grid of numbers with a row and column sum of 30 is

3 15 12

17 11 2

10 4 16

<h3>How to prepare the grid?</h3>

The grid in the question has a row sum and column sum of 15

The question implies that we create a similar grid with a row sum and column sum of 30

Represent the grid as follows:

a b c

d e f

g h j

So, we have the following sum of rows

a + b + c = 30

d + e + f = 30

g + h + j = 30

And, we have the following sum of rows

a + d + g = 30

b + e + h = 30

c + f + j = 30

Using trial by error, we have:

3 + 15+ 12 = 30

17 + 11 + 2 = 30

10 + 4 + 16 = 30

When the columns are added, we have

3 + 17 + 10 = 30

15 + 11 + 4 = 30

12 + 2 + 16 = 30

Hence, the grid of numbers is

3 15 12

17 11 2

10 4 16

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To prove this, draw a line from each corner to the "center" where the four lines meet. Along each side of the square are two triangles. These triangles have the same base and the same height, and therefore have the same area.

If we say the triangles at the bottom have area a, the triangles on the left have area b, the triangles on top have area c, and the triangles on the right have area d, then we can write 4 equations:

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