Page 297 - Ganit Kaushal

2. 5 supercells, those which are coloured green. 4. Yes, this is possible. Make them stand in a line in
 n +  1  n increasing order of their height. Then first four will
3.   if ‘n’ is odd, and,   if ‘n’ is even; where
 2   2 say ‘1’ and the last one will say 0’. (See figure)
‘n’ is total no. of cells in the table. 1 0

4. Yes, there is a pattern. Supercells can only occur 1 1
alternatively. They can’t be consecutive. Therefore, 1
to get maximum number of super cells, get them
alternatively.

5. No, at least one supercell is always there (because the
cell with greatest number is always a supercell).

6. Yes, because the largest number of the table will be So, the sequence of numbers we get will be 1, 1, 1, 1, 0.
larger than its neighbouring cells. No, because the 5. No, the sequence 1, 1, 1, 1, 1 is not possible.
smallest number of the table will not be larger than its

neighbouring cells. 6. Yes, the sequence 0, 1, 2, 1, 0 is possible. Make them
stand in decreasing order of height up to third child
7. 100 105 120 124 130 136 140 150 145 then in increasing order till 5th child. (as in the picture)
Here, the second largest number is 145 which is not a
supercell.
8. Yes, it is possible. See the table below.

114 100 120 125 130 135 140 150 145
Here, second largest number is 145 which is not a super
cell, 114 is the second smallest number and it is a super
cell. Blue coloured are supercells.
7. The arrangement of sequence so that maximum children

NOTE: This can be done by putting these numbers at the extremes
of the table say ‘2’ will be 0, 2, 0, 2, 0. Because the children at the
9. After completion Table 2 is as given here. end can never say ‘2’. Also, two children standing next
Table 2 to each other cannot say ‘0’ as well as ‘2’. So, we cannot
have two consecutive 0’s as well as two consecutive 2’s.
96,310 96,301 36,109 36,190 so the only possibility left is 0, 2, 0, 2, 0.
63,019 13,609 60,319 19,306 Exercise 3.4
60,139 10,369 60,193 36,019 1. 7- rounds
10,396 10,963 10,639 36,910 2. (a) 4, 7, 3, 1; 7431 – 1347 = 6084 > 5085
(a) 96,310; Ninety-six thousand three hundred and (b) 6, 4, 3, 2; 6432 – 2346 = 4086 < 5085
ten. (c) 7, 5, 3, 2; 7532 + 2357 = 9889 > 9779
(b) 10,396; Ten thousand three hundred and ninety- (d) 7, 4, 3, 1; 7431 + 1347 = 8778 < 9779
six. 3. 495; (This is known as ‘Kaprekar Constant’ for

(c) 10,369; Ten thousand three hundred and sixty- 3 digits numbers. Students are advised to start with
nine. 3-digit numbers of their own choice and observe this
(d) 60,139; Sixty thousand one hundred and thirty- repetition.)
nine. 4. The number is 12,421.
(e) 36,910; Thirty-Six thousand nine hundred and The complete form of table is given here:
ten. TTh Th H T U
(f) Commas has been put in the table according to 1 2 4 2 1
Indian system of numeration. (Answer may vary)
Twelve Thousand Four
Exercise 3.3 Hundred and Twenty-One.

1. No. The child at the end can never say ‘2’. Because of
the simple reason of having only one neighbour. So, 5. 01/02/2010; 11/02/2011; 21/02/2012; 02/02/2020.
either he can say one or zero.
2. No, this is not possible. 6. 93039, 84048, 75057, 66066, 57075, 48084, 39093

3. Yes, this is possible. Two children standing next to each 7. 56665, 56765, 56865, 56965, 57075, 57175, 57275,

th
other can say the same number ‘1’, if they are lined up 57375; 8 term = 57375.
in increasing order of their height. 8. 99, 101 9. 232
Answers 295