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So, sum of 2nd row = 3 + (–1) + ? = –3

Or, 2 + ? = –3
Clearly, in the blank space of 2nd row, we have to fill –5 to get the magic sum –3.
Apply the same logic, so that the sum of rows, columns and diagonals equals to –3.

Thus, the magic square would be:

–4 1 0

3 –1 –5

–2 –3 2

Striking Magic Grid 3 4 0 9

Here is a 4 by 4 magic grid. Do not confuse it with a magic square. You have
to select any number of the grid and circle it. Strike out the row and column –2 –1 –5 4
containing the chosen number. Repeat the process until all numbers are 1 2 –2 7
struck out. Add all the circled numbers. In all the cases you will get the same
result. –7 –6 –10 –1
Let’s understand it with the example.

Step 1: We first circle (–5) and strike out the row Step 2: Next, we circle number 3 and strike out
and column containing it. the row and column containing it.

3 4 0 9 3 4 0 9

–2 –1 –5 4 –2 –1 –5 4

1 2 –2 7 1 2 –2 7

–7 –6 –10 –1 –7 –6 –10 –1
Step 3: Then, we circle the number (–1) and Step 4: Now, we are left with one row. Circle 2
strike out the row and column containing it. and strike out the row and column containing it.

3 4 0 9 3 4 0 9

–2 –1 –5 4 –2 –1 –5 4

1 2 –2 7 1 2 –2 7

–7 –6 –10 –1 –7 –6 –10 –1

Therefore, the sum of the circled numbers = 3 + (–5) + 2 + (–1) = –1.
Practice Time 10D

1. Write all the integers between the given pairs in increasing order

(a) 0 and –7 (b) –30 and –23 (c) –8 and –15 (d) –235 and –250
(e) –3 and +3 (f) 4 and 16

297 The Other Side of Zero