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NCERT Solutions Ganita Prakash (Part 1) Chapter 1 .2 Land of Tens — In-text Questions

Book page 71 Updated on2026-09-05

Q1.
Creative Chitti has some questions for you — (a) You have to make exactly 30 button presses. What is the largest 3-digit number you can make? What is the smallest 3-digit number you can make?
Answer

Largest = 993. Smallest = 102.

Largest: put as many presses as possible on +100.
(9 × 100) + (8 × 10) + (13 × 1)
= 900 + 80 + 13 = 993
Presses = 9 + 8 + 13 = 30 ✓

Smallest: put as few presses as possible on +100.
(0 × 100) + (8 × 10) + (22 × 1)
= 0 + 80 + 22 = 102
Presses = 0 + 8 + 22 = 30 ✓
Why it happens: With 30 presses fixed, moving one press from +1 to +100 adds 99 to the number. So to go large you load the +100 button — but you cannot press it 10 times (that alone is 1000, a 4-digit number), so 9 is the limit; the remaining 21 presses must make 93, and 8 tens + 13 ones does it. To go small you avoid +100 altogether; 30 presses of tens and ones must still reach at least 100, and 8 tens + 22 ones = 102 is the least such total.
Check it yourself: Could 101 be made? It would need 1 hundred + 0 tens + 1 one (2 presses) or 10 tens + 1 one (11 presses) — neither is 30, and no other split of 101 uses 30 presses. So 102 really is the smallest.
Q2.
997 can be made using 25 clicks. Can you make 997 with a different number of clicks?
Answer

Yes — 997 can be made with many different click counts.

25 clicks: (9 × 100) + (9 × 10) + (7 × 1) = 900 + 90 + 7 = 997
Clicks = 9 + 9 + 7 = 25

34 clicks: (9 × 100) + (8 × 10) + (17 × 1) = 900 + 80 + 17 = 997
Clicks = 9 + 8 + 17 = 34

106 clicks: (99 × 10) + (7 × 1) = 990 + 7 = 997
Clicks = 99 + 7 = 106

997 clicks: (997 × 1) = 997
Why it happens: Trading one +100 press for ten +10 presses keeps the total the same but adds 9 clicks; trading one +10 for ten +1 also adds 9 clicks. So every possible click count for 997 is 25, 34, 43, 52, … — always 25 plus a multiple of 9. The smallest is 25 (the digit sum) and the largest is 997.
Q3.
Systematic Sippy has the buttons +1, +10, +100, +1000, +10000, +100000. It wants to be used as minimally as possible. How can we get the numbers (a) 5072, (b) 8300 using as few button clicks as possible? Also: the table shows one way to get 5072 using 23 button clicks. Is there another way to get 5072 using less than 23 button clicks? Write the expression for the same.
Answer

Yes. 5072 can be made in just 14 clicks, and 8300 in 11 clicks.

(a) 5072 = (5 × 1000) + (0 × 100) + (7 × 10) + (2 × 1)
Clicks = 5 + 0 + 7 + 2 = 14

(b) 8300 = (8 × 1000) + (3 × 100) + (0 × 10) + (0 × 1)
Clicks = 8 + 3 + 0 + 0 = 11

The table's method used (5 × 1000) + (0 × 100) + (6 × 10) + (12 × 1) = 5000 + 60 + 12 = 5072, which is 5 + 0 + 6 + 12 = 23 clicks. Replacing 6 tens and 12 ones by 7 tens and 2 ones saves 9 clicks.

Why it happens: Every time you use ten small presses where one big press would do, you waste 9 clicks. The cheapest route is therefore to use each button no more than 9 times — and that is exactly what the digits of the number tell you to do.
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