Page 73 - Ganit Kaushal

10. Find out how many numbers have two digits, three digits, four digits and five digits and complete the
following table:

1-digit numbers 2-digit numbers 3-digit numbers 4-digit numbers 5-digit numbers
From: 1-9

9

11. Calculate the digit sums of 3-digit numbers whose digits are consecutive (for example, 345). Do you
see a pattern? (NCERT)
12. What is the smallest number whose digit sum is 14? (NCERT)
13. What is the largest 5-digit number whose digit sum is 14? (NCERT)

14. How big a number can you form having the digit sum 14? Can you make an even bigger number?
(NCERT)
15. Among the numbers 1 to 100, how many times will the digit 7 occur? (NCERT)
16. Among the numbers 1 to 1000, how many times will the digit 7 occur? (NCERT)

17. Divide the following. Find the quotient and remainder. Write the result in a division algorithm form.
(a) 879 by 13 (b) 7750 by 17
18. Find the number which when divided by 33 gives the quotient 21 and remainder 14.

19. Which least number should be subtracted from 1000 such that the difference is exactly divisible by
35?
20. Find the smallest 5-digit number that is exactly divisible by 254.
21. Find the largest 3-digit number that is exactly divisible by 47.

22. Which least number should be added to 1000 so that the sum is exactly divisible by 53?

3.7 GAME OF SUPERCELLS

Let us make a row of cells and place some numbers in each cell. A cell is called a Supercell if the number in
it is larger than its neighbouring cells. We will colour that cell just to distinguish it from others.

43 79 75 59 10 29 21 34

191 577 626 305 790 581 109 198

For example: In the first row given above, 79 is coloured as it is larger than its neighbouring cells, 43 and 75.
So, 79 is a supercell. Similarly, 29 is coloured as it is larger than its neighbouring cells, 10 and 21. The number
34 is larger than its only one neighbouring cell 21.

Similarly, in the second row, 626, 790, and 198 are supercells.
Can we have two consecutive supercells?
Great! you got it right. The answer is no. We cannot have two consecutive supercells. The reason for
this is simple: since a supercell contains a number larger than its neighbouring cells, the neighbouring
cell cannot be larger than at least one of its left or right neighbours.

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