NCERT Solutions Ganita Prakash (Part 1) Chapter 2 .2 Exponential Notation and Operations · The Stones that Shine … — In-text Questions
Book page 232 Updated on2026-09-05
Q1.
Three daughters with curious eyes, / Each got three baskets — a kingly prize. / Each basket had three silver keys, / Each opens three big rooms with ease. / Each room had tables — one, two, three, / With three bright necklaces on each, you see. / Each necklace had three diamonds so fine… / Can you count these stones that shine? [Hint: Find out the number of baskets and rooms.]
Answer
37 = 2187 diamonds.
Follow the riddle level by level. Each line multiplies the count by 3.
Level
Count
Value
daughters
3
31 = 3
baskets
3 × 3
32 = 9
keys
3 × 3 × 3
33 = 27
rooms
3 × 3 × 3 × 3
34 = 81
tables
35
243
necklaces
36
729
diamonds
37
2187
Why it happens: the riddle has seven "each … three" steps, one per level. Every step multiplies by 3, so the total is 3 multiplied by itself 7 times. The exponent is simply a count of the levels — which is why exponential notation is the natural language for anything that branches.
Why it happens: rooms sit four branchings below the king — daughters, baskets, keys, rooms — so the exponent is 4. Counting the levels is faster and safer than drawing all 81 rooms, and it is the only method that still works when the levels number 20 instead of 4.
Q3.
How many diamonds were there in total? Can we find out by just one multiplication using the products above?
Answer
Yes — 2187 diamonds, from a single multiplication.
Number of diamonds = 3 × 3 × 3 × 3 × 3 × 3 × 3 = 37 Split the seven 3s as four and three: 37 = (3 × 3 × 3 × 3) × (3 × 3 × 3) = 34 × 33 = 81 × 27 = 2187
We had already reached 81 while counting the rooms, and 27 while counting the keys. So one multiplication, 81 × 27, finishes the job.
Why it happens: this is the first appearance of the product rule. Seven copies of 3 can be split into a group of 4 and a group of 3 in the multiplication, because multiplication lets you regroup freely. The exponents therefore add: 34 × 33 = 34+3 = 37. In general na × nb = na+b.