Should we check every number pair to find out which is the largest sum or difference? 35 100 179 68 111 185 143 54 300 48 225 190 54 321 63 167 The number grid printed on page 112.

35 100 179 68 111 185 143 54 300 48 225 190 54 321 63 167 The number grid printed on page 112. No. We need not check all 24 pairs. For the largest sum , look only at the big numbers — 300, 321, 225, 190, 185 — and check the pairs they make with their neighbours. For the largest difference , look for a big number sitting next to a small one, like 321 next to 48. For the smallest sum , look only at the small numbers — 35, 48, 54, 63, 68. For the smallest difference , look for two neighbours that are close in size, like 68 and 54. Why it happens: A pair of small numbers can never give a big sum, so those pairs can be left out straight away.

NCERT Solutions for Class 4th Maths Chapter 7 The grid of numbers — Number Pair Hunt

Book page 112 to 113 Updated on2026-09-19

Q1.

How many number pairs are there in this grid?

35	100	179	68
111	185	143	54
300	48	225	190
54	321	63	167

The number grid printed on page 112.

Answer

35	100	179	68
111	185	143	54
300	48	225	190
54	321	63	167

The number grid printed on page 112.

There are 24 number pairs.

Side by side (across): 4 rows × 3 pairs = 12
One above the other (down): 4 columns × 3 pairs = 12
12 + 12 = 24

Why it happens: In a row of 4 numbers there are only 3 places where two numbers touch. The same is true going down.

Tip: Corner-to-corner numbers are not a pair. Only across and down count.

Q2.

Should we check every number pair to find out which is the largest sum or difference?

35	100	179	68
111	185	143	54
300	48	225	190
54	321	63	167

The number grid printed on page 112.

Answer

35	100	179	68
111	185	143	54
300	48	225	190
54	321	63	167

The number grid printed on page 112.

No. We need not check all 24 pairs.

For the largest sum, look only at the big numbers — 300, 321, 225, 190, 185 — and check the pairs they make with their neighbours.
For the largest difference, look for a big number sitting next to a small one, like 321 next to 48.
For the smallest sum, look only at the small numbers — 35, 48, 54, 63, 68.
For the smallest difference, look for two neighbours that are close in size, like 68 and 54.

Why it happens: A pair of small numbers can never give a big sum, so those pairs can be left out straight away.

Q3.

1. Find the number pair whose sum is the greatest.

35	100	179	68
111	185	143	54
300	48	225	190
54	321	63	167

The number grid printed on page 112.

Answer

35	100	179	68
111	185	143	54
300	48	225	190
54	321	63	167

The number grid printed on page 112.

The pair is 225 and 190. Their sum is 415.

The working, written in columns.

Other big pairs:
111 + 300 = 411
300 + 48 = 348
321 + 63 = 384
225 + 190 = 415 is the biggest

Why it happens: 300 and 321 are bigger numbers, but every neighbour they have is small. 225 and 190 are both large and they sit side by side.

Q4.

2. Find the number pair whose sum is the smallest.

35	100	179	68
111	185	143	54
300	48	225	190
54	321	63	167

The number grid printed on page 112.

Answer

35	100	179	68
111	185	143	54
300	48	225	190
54	321	63	167

The number grid printed on page 112.

The pair is 68 and 54. Their sum is 122.

The working, written in columns.

Other small pairs:
35 + 100 = 135
35 + 111 = 146
63 + 167 = 230
68 + 54 = 122 is the smallest

Why it happens: 68 and 54 are two of the smallest numbers in the grid, and luckily they are neighbours in the last column.

Q5.

3. Find the number pair whose difference is the greatest.

35	100	179	68
111	185	143	54
300	48	225	190
54	321	63	167

The number grid printed on page 112.

Answer

35	100	179	68
111	185	143	54
300	48	225	190
54	321	63	167

The number grid printed on page 112.

The pair is 321 and 48. Their difference is 273.

The working, written in columns.

Other big differences:
321 − 54 = 267
300 − 48 = 252
300 − 54 = 246
321 − 48 = 273 is the biggest

Why it happens: 321 is the biggest number in the grid and 48 is one of the smallest, and the two sit one above the other.

Q6.

4. Find the number pair whose difference is the smallest.

35	100	179	68
111	185	143	54
300	48	225	190
54	321	63	167

The number grid printed on page 112.

Answer

35	100	179	68
111	185	143	54
300	48	225	190
54	321	63	167

The number grid printed on page 112.

The pair is 68 and 54. Their difference is 14.

The working, written in columns.

Other small differences:
190 − 167 = 23
225 − 190 = 35
179 − 143 = 36
68 − 54 = 14 is the smallest

Why it happens: The smallest difference comes from two neighbours that are nearly the same size, and 68 and 54 are only 14 apart.

Did you know? The same pair, 68 and 54, gives both the smallest sum and the smallest difference.

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