NCERT Solutions Ganita Prakash (Part 1) Chapter 2 Puzzle Time! Tremendous in Ten! — In-text Questions

Book page 47 Updated on2026-09-05

Q1.

In Round 1, Roxie wrote 10000000000000 and Estu wrote 999999 × 999999. Between these two, Roxie’s number is greater. Can you see why?

Answer

Compare the two as powers of 10, without multiplying anything out.

Roxie: 10000000000000 = 1 followed by 13 zeros = 10¹³

Estu: 999999 < 10⁶, so
999999 × 999999 < 10⁶ × 10⁶ = (10⁶)² = 10¹²

So Estu's number < 10¹² < 10¹³ = Roxie's number ✓

Estu's number is in fact 9,99,99,80,00,001 ≈ 9.99998 × 10¹¹ — just under a lakh crore, while Roxie's is ten lakh crore.

Why it happens: Estu spent his ten seconds on digits that look impressive but only reach 10¹²; Roxie spent hers on zeros, and each zero multiplies by 10. Within the rules of Round 1 — no exponents allowed — writing zeros is the fastest way to grow, because each keystroke buys a factor of 10 while a multiplication sign buys nothing on its own.

Q2.

In Round 2, Roxie wrote 10¹⁰⁰⁰ + 10¹⁰⁰⁰ + 10¹⁰⁰⁰ + 10¹⁰⁰⁰ and Estu wrote (10¹⁰⁰⁰⁰⁰⁰) × 9000. Can you say which is greater?

Answer

Estu's number is greater — overwhelmingly so.

Roxie: 10¹⁰⁰⁰ + 10¹⁰⁰⁰ + 10¹⁰⁰⁰ + 10¹⁰⁰⁰
= (1 + 1 + 1 + 1) × 10¹⁰⁰⁰
= 4 × 10¹⁰⁰⁰

Estu: 10^1000000 × 9000
= 9 × 10³ × 10^1000000
= 9 × 10^1000003

Ratio = (9 × 10^1000003) ÷ (4 × 10¹⁰⁰⁰)
= 2.25 × 10^{1000003 – 1000}
= 2.25 × 10⁹⁹⁹⁰⁰³ times bigger

Why it happens: adding four copies of a number multiplies it by 4 — it moves the coefficient, and leaves the exponent alone. Estu instead raised the exponent from 1000 to 10,00,000, and the exponent is where all the size lives. This is the chapter's central lesson in one line: when the numbers are large, the exponent decides, and the coefficient is only a detail.

Try This: play a round with the rule "exponents allowed, only addition allowed". Now nobody can multiply, so the winner is whoever writes the biggest single power — and 9⁹⁹ beats 99⁹, since 9⁹⁹ ≈ 3 × 10⁹⁴ while 99⁹ ≈ 9 × 10¹⁷. The exponent wins again.

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