NCERT Solutions Ganita Prakash Chapter 3 In-text Questions — Numbers can Tell us Things

Book page 56 Updated on2026-09-05

Q1.

Can the children rearrange themselves so that the children standing at the ends say ‘2’?

Answer

No, it is impossible.

Why it happens: a child standing at an end of the line has only one neighbour — there is nobody on the outer side. Saying ‘2’ means “both my neighbours are taller”, but an end child does not even have two neighbours. So a child at an end can only say 0 or 1.

Q2.

Can we arrange the children in a line so that all would say only 0s?

Answer

Yes — but only if all the children are of the same height.

If everybody is equally tall, then nobody has a taller neighbour, so every child says 0.

Why nothing else works: suppose the heights are not all equal. Take the shortest child in the line. Somebody standing next to that child is taller, so the shortest child would have to say 1 or 2 — not 0.

Q3.

Can two children standing next to each other say the same number?

Answer

Yes. Two neighbours can easily say the same number.

Look at the very first picture on page 55: the children say 0, 2, 1, 1, 0, 2, 1, 0 — the third and the fourth child both say ‘1’.

This happens when the children are standing in increasing order of height:

shortest → taller → taller → taller → tallest
numbers said: 1, 1, 1, 1, 0

Here the first four children each have exactly one taller neighbour (the one on their right).

Q4.

There are 5 children in a group, all of different heights. Can they stand such that four of them say ‘1’ and the last one says ‘0’? Why or why not?

Answer

Yes, they can. Make them stand in order of height — shortest to tallest.

Five children of different heights standing in increasing order. The first four each have exactly one taller neighbour, so they say 1; the tallest says 0.

Why it works: for each of the first four children the neighbour on the right is taller and the neighbour on the left (if any) is shorter — that is exactly one taller neighbour. The tallest child stands at the end and has nobody taller beside him, so he says 0.

Q5.

For this group of 5 children, is the sequence 1, 1, 1, 1, 1 possible?

Answer

No, it is not possible.

Why it happens: think about the tallest child of the group. Nobody is taller than that child, so whatever place the tallest child takes in the line, he or she must say 0. A ‘0’ must therefore appear somewhere in the sequence, and so all five children can never say 1.

Tip: the same reasoning shows that the sequence can never be all 1s or all 2s for any number of children with different heights — a 0 always appears where the tallest child stands.

Q6.

Is the sequence 0, 1, 2, 1, 0 possible? Why or why not?

Answer

Yes, it is possible. Arrange the children so that the two tallest stand at the two ends and the shortest stands in the middle.

Heights going down towards the middle and up again. The middle child is shorter than both neighbours, so she says 2.

Say the heights (in cm) are 150, 140, 120, 130, 145 from left to right:

150 → right neighbour 140 is shorter → says 0
140 → 150 is taller, 120 is shorter → says 1
120 → both 140 and 130 are taller → says 2
130 → 120 is shorter, 145 is taller → says 1
145 → 130 is shorter → says 0

Q7.

How would you rearrange the five children so that the maximum number of children say ‘2’?

Answer

At most two children out of five can say ‘2’. Arrange them so that the two shortest children stand in the 2nd and 4th places, with taller children on both sides of each:

Heights 145, 120, 150, 125, 140. The 2nd and 4th children are shorter than both their neighbours, so each says 2 — the sequence is 0, 2, 0, 2, 0.

Why only two: the children at the two ends can never say 2, so only the 2nd, 3rd and 4th children are possible. But two children saying ‘2’ can never stand next to each other — if the 3rd child said 2, the 2nd and 4th would both be taller than him and could not say 2 themselves. So the best we can do is the 2nd and the 4th: 2 children.

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