Question

Do you remember magic triangles? Come now, let s make some magic squares.

• Fill this square using all the numbers from 46 to 54.
  Rule: The total of each line is 150.
  

Answer 1

Given that the total of each line = 150

We can use numbers from 46 to 54.

• In the third row, we have
  a + 52 + 47 = 150
  a + 99 = 150
  a = 150 – 99 = 51

So, we can fill 51 in the first box of the third row.

• Now, in the first column, we have
  b + 46 + 51 = 150
  b + 97 = 150
  b = 150 – 97 = 53

So, we can fill 53 in the first box of the first column.

• In the first row, we have
  53 + c + 49 = 150
  c + 102 = 150
  c = 150 – 102 = 48

So, we can fill 48 in the second box of the first row.

• In the second column, we have
  48 + d + 52 = 150
  d + 100 = 150
  d = 150 – 100 = 50

So, we can fill 50 in the second box of the second column.

• In the third column, we have
  49 + e + 47 = 150
  e + 96 = 150
  e = 150 – 96 = 54

So, we can fill 54 in the second box of the third column.

The box with all values is given below: