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2. Complete the grid.

(a) (b) (c)
–10 6 8 7

–5 –5 –5

9 –2

Border sum is +4. Border sum is –2. Border sum is –4.
3. Complete the following integer magic squares:

(a) (b)
–6 –7

–7 –5 –3 –2

–4 –1 –3

4. There are two dice whose faces have these numbers: –1, 2, –3, 4, –5 and 6. The smallest possible
sum upon rolling these dice is –10 {(–5) + (–5)} and the largest possible sum is 12 (6 + 6). Between
–10 and 12, some numbers can’t be obtained by adding the numbers that appeared on the faces of
the dice. Find those impossible numbers.

5. For the given magic grid, select the number and strike out the row and column containing it.
Repeat the process till all rows and columns are struck out. Find the sum of the circled numbers.

(a) (b) (c)
3 –2 1 –7 7 –2 –11 –20 –11 –7 –3 1

4 –1 2 –6 10 1 –8 –7 –10 –6 –2 2

0 –5 –2 –10 13 4 –5 –14 –9 –5 –1 3

9 –4 7 –1 16 7 –2 –11 –8 –4 0 4

Mental Maths
1. Complete the following magic square:
(a) (b) (c) (d)
0 5 –2 –4 –4 2

–1 –1 1 5 1

4 –3 2 2 0
2. Here are six integers: (+1), (+7), (+18), (–5), (–2), (–9). You can choose any four of these and make an expression
using addition(s) and subtraction(s). Here is an expression: (+18) + (–5) – (+7) – (–9) which gives a value (+15).
Now, pick integers and make an expression such that its value is closer to (–20).
3. The sum of two positive integers is always positive but a (positive integer) – (positive integer) can be positive
or negative. What about:
(a) (positive) – (negative) (b) (positive) + (negative) (c) (negative) + (negative)
(d) (negative) – (negative) (e) (negative) – (positive) (f) (negative) + (positive)

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