Page 76 - Ganit Kaushal

3.8 GAME OF HEIGHTS

Whole numbers can tell us various things; they are not just used
for counting.
For example: They can tell us the comparison of heights among
friends. Look at the adjoining picture where some friends are
standing in a line in a park and they are shouting some numbers 0,
1, and 2.
Now, the friends have rearranged themselves. And again, they are
shouting the same numbers 0, 1 and 2, as shown in the figure below.
What do you think, they are doing? Any guesses.

Yes, your guess is right. They are playing a game related to
their heights.

They have decided that:
A child will say ‘1’, if in his/her neighbourhood there is only one child taller than him/her.

A child will say ‘2’, if in his/her neighbourhood there are two children taller than him/her.
A child will say ‘0’, if in his/her neighbourhood no one is taller than them.

So, you may understand that each of them is shouting the number of taller neighbours they have.
This is a very interesting game. Every time the children rearrange themselves and say the numbers 0, 1 or 2,
telling the number of taller neighbours they have.
Many mind-boggling questions can be raised regarding this game now. Like-

Is it possible for children standing at the corners to shout ‘2’?
Is it possible that two children standing next to each other shout ‘2’?
Is it possible that two children
standing next to each other shout Remember
‘1’? 1. Corner children can never shout ‘2’.
Is it possible that two children 2. There can’t be two consecutive children shouting 2.
standing next to each other shout 3. There can’t be two consecutive children shouting 0.
‘0’? 4. We can have two or more consecutive children shouting 1.

Exercise 3.3

1. Can the children rearrange themselves so that the children standing at the ends say ‘2’?
2. Can we arrange the children in a line so that all would say only 0s?
3. Can two children standing next to each other say the same number?

4. 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?

5. For this group of 5 children, is the sequence 1, 1, 1, 1, 1 possible?
6. Is the sequence 0, 1, 2, 1, 0 possible? Why or why not?
7. How would you rearrange the five children so that the maximum number of children say ‘2’?

74 Mathematics-6