NCERT Solutions Ganita Prakash (Part 1) Chapter 6 Figure it Out — Numbers Tell us Things

Book page 128 Updated on2026-09-05

Q1.

Arrange the stick figure cutouts given at the end of the book or draw a height arrangement such that the sequence reads: (a) 0, 1, 1, 2, 4, 1, 5 (b) 0, 0, 0, 0, 0, 0, 0 (c) 0, 1, 2, 3, 4, 5, 6 (d) 0, 1, 0, 1, 0, 1, 0 (e) 0, 1, 1, 1, 1, 1, 1 (f) 0, 0, 0, 3, 3, 3, 3

Answer

Give the seven cutouts heights 1 to 7, where 7 is the tallest and 1 is the shortest. Then arrange them left to right as shown.

Sequence to be read out	Heights from left to right (7 = tallest)
(a) 0, 1, 1, 2, 4, 1, 5	7, 3, 5, 4, 1, 6, 2
(b) 0, 0, 0, 0, 0, 0, 0	1, 2, 3, 4, 5, 6, 7
(c) 0, 1, 2, 3, 4, 5, 6	7, 6, 5, 4, 3, 2, 1
(d) 0, 1, 0, 1, 0, 1, 0	2, 1, 4, 3, 6, 5, 7
(e) 0, 1, 1, 1, 1, 1, 1	7, 1, 2, 3, 4, 5, 6
(f) 0, 0, 0, 3, 3, 3, 3	5, 6, 7, 1, 2, 3, 4

Check (a) child by child:

7 → nobody ahead = 0
3 → taller ahead: 7 = 1
5 → taller ahead: 7 = 1
4 → taller ahead: 7, 5 = 2
1 → taller ahead: 7, 3, 5, 4 = 4
6 → taller ahead: 7 = 1
2 → taller ahead: 7, 3, 5, 4, 6 = 5

And check (f): heights 5, 6, 7, 1, 2, 3, 4 give 0, 0, 0, 3, 3, 3, 3, because the first three are taller than each of the last four.

Why it happens: build the line from the last child backwards. If a child must say k, then exactly k of the children already placed ahead must be taller — so that child is the (k + 1)th tallest among those in front of it plus itself. Each sequence in this question fixes the whole order of heights, so there is only one height order for each part.

Try This: not every list is possible. A list like 0, 2, 0, 0, 0, 0, 0 can never happen, because the second child has only one child ahead and cannot see two taller people.

Q2.

For each of the statements given below, think and identify if it is Always True, Only Sometimes True, or Never True. Share your reasoning. (a) If a person says ‘0’, then they are the tallest in the group. (b) If a person is the tallest, then their number is ‘0’. (c) The first person’s number is ‘0’. (d) If a person is not first or last in line (i.e., if they are standing somewhere in between), then they cannot say ‘0’. (e) The person who calls out the largest number is the shortest. (f) What is the largest number possible in a group of 8 people?

Answer

Statement	Answer	Reason
(a) Says ‘0’ ⇒ tallest in the group	Only Sometimes True	Saying 0 only means nobody ahead is taller. The first child always says 0 even if he is the shortest of all.
(b) Tallest ⇒ number is ‘0’	Always True	Nobody in the whole line is taller, so certainly nobody ahead is taller.
(c) First person’s number is ‘0’	Always True	There is nobody in front of the first person to count.
(d) A person in between cannot say ‘0’	Only Sometimes True	A middle child says 0 whenever he is taller than everybody ahead of him — as the third child does in 5, 6, 7, 1, 2, 3, 4.
(e) Largest number ⇒ shortest person	Only Sometimes True	In 7, 3, 5, 4, 1, 6, 2 the largest number 5 is said by the second-shortest child, not the shortest.

(f) The largest number possible in a group of 8 people is 7.

Only the children ahead of you can be counted.
The 8th (last) child has 7 children in front.
At best all 7 are taller → largest number = 7

Why it happens: a child standing at position p can say at most p – 1. So in a group of n people the biggest number anybody can say is n – 1, and it happens only when the last child is the shortest.

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