Page 75 - Ganit Kaushal

Example: Observe the grid given in Table-2; there is only one supercell in this 35,999 39,333 20,766
grid, namely 82,677 (the shaded one). 63,609 82,677 54,306

Can we increase the number of supercells to 4 by interchanging two digits 49,381 50,318 34,084
of one of the numbers? Table-2
Yes! We can. Interchange the digits 8 and 2 of the supercell, and we 35,999 39,333 20,766
observe the new grid has 4 supercells (Table-3, the four shaded cells are 63,609 28,677 54,306
supercells).
49,381 50,318 34,084
Amazing! isn’t it? Table-3

Exercise 3.2

1. Fill in the table below such that we get as many supercells as possible. Use numbers between 100 and
1000 without repetitions. (NCERT)

2. Out of the 9 cells, how many supercells are there in the table above in ques-1? (NCERT)
(Hint: Use answer to ques-3, by taking n = 9)
3. Find out how many supercells are possible for different numbers of cells. (NCERT)
(Hint: Two consecutive cells can’t be supercells)

4. Do you notice any pattern while filling in the above table to get maximum supercells? What is the
method to fill a given table to get the maximum number of supercells? (NCERT)
5. Can you fill a supercell table without repeating numbers such that there are no supercells? Why or
why not? (NCERT)

6. Will the cell having the largest number in a table always be a supercell? Can the cell having the smallest
number in a table be a supercell? Why or why not? (NCERT)
7. Fill a table such that the cell having the second largest number is not a supercell. (NCERT)
8. Fill a table such that the cell having the second largest number is not a supercell, but the 2nd smallest
number is a supercell. Is it possible?

9. Complete Table 4 with 5-digit numbers whose digits are 1, 0, 6, Table-4
3, and 9 in some order. The table should be completed in such a 96,301 36,109
manner that all coloured cells should become the supercells. Then 13,609 60,319 19,306
associated to this table, answer the following. (NCERT) 60,193
(a) What is the biggest number in the table? Write it in 10,963
numerals and words.
(b) What is the smallest even number in the table? Write it in numerals and words.

(c) What is the smallest odd number in the table? Write it in numerals and words.
(d) What is the smallest number greater than 50,000 in the table? Write it in numerals and words.
(e) What is the largest number less than 50,000 in the table? Write it in numerals and words.

(f) After filling in the above table, put commas appropriately according to the Indian system of
numeration.

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