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Class 6 Maths: Number Play, 8 practice questions with answers

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These are 8 practice questions on Class 6 Maths Chapter 3, Number Play, of the new NCERT textbook, Ganita Prakash. Each has a worked answer and the textbook page it comes from. They cover counting taller neighbours, supercells, palindromes and reverse-and-add, Kaprekar's steps, the Collatz rule, estimating, and quick ways to add. Try each one on paper before you open the answer.

These questions are our own, drafted with AI help. Every number was re-computed by a test script, and no starting number is taken from the chapter, checked against its text and its figure pages (a few results, such as the Kaprekar constant 6174, appear there too), but no practising teacher has reviewed them yet. If you find a mistake, please tell us.

What the chapter says you need

Facts from the NCERT textbook (Ganita Prakash: Textbook of Mathematics for Grade 6, Chapter 3, printed pages 55 to 73):

Numbers that tell us things

Question 1. Five children stand in a line. Their heights, in order, are 129 cm, 124 cm, 147 cm, 117 cm and 138 cm. Each child says the number of taller neighbours they have. What does each child say?

Answer: 0, 2, 0, 2, 0. The 129 cm child has one neighbour, 124 cm, who is shorter: 0. The 124 cm child has neighbours 129 cm and 147 cm, both taller: 2. The 147 cm child has neighbours 124 cm and 117 cm, both shorter: 0. The 117 cm child has neighbours 147 cm and 138 cm, both taller: 2. The 138 cm child at the end has one neighbour, 117 cm, who is shorter: 0. (Taller neighbours, page 56.)

Question 2. A row of cells reads 4,812 | 5,307 | 5,290 | 6,014 | 3,955. Asha marks 4,812 as a supercell "because it is bigger than 3,955". Find her mistake, and say which cells are supercells.

Answer: a supercell is compared only with its neighbouring cells; the supercells are 5,307 and 6,014. 4,812 has only one neighbour, 5,307, and it is smaller than 5,307, so it is not a supercell; 3,955 is not its neighbour at all. 5,307 is larger than both its neighbours, 4,812 and 5,290. 5,290 is smaller than 5,307. 6,014 is larger than both 5,290 and 3,955. 3,955 is smaller than its only neighbour, 6,014. (Supercells, page 57.)

Playing with digits

Question 3. (a) Which of these are palindromes: 4,554; 4,545; 37,073; 37,037? (b) Ravi starts with 69 and reverse-and-adds: 69 + 96 = 165, then 165 + 561 = 726. He says 726 is a palindrome, so he stops. Find his mistake and finish the steps. How many additions does it take in all?

Answer: (a) 4,554 and 37,073. (b) Ravi stopped too early: it takes four additions. (a) 4,554 and 37,073 read the same from either end; 4,545 read backwards is 5,454, and 37,037 read backwards is 73,073, so those two are not palindromes. (b) 726 read backwards is 627, so it is not a palindrome; four additions: 69 + 96 = 165, 165 + 561 = 726, 726 + 627 = 1,353, then 1,353 + 3,531 = 4,884, which reads the same both ways. (Palindromes and reverse-and-add, page 61.)

Question 4. Sana tries Kaprekar's steps with 3,333 and gets 3,333 − 3,333 = 0 straight away. Which rule did she miss? Which of 3,333, 4,334 and 2,220 can be used to start?

Answer: the starting number must have at least two different digits; 4,334 and 2,220 can be used, 3,333 cannot. If all four digits are the same, the largest and smallest numbers made from them are equal, so the difference is 0 and the steps never reach 6174. 4,334 (digits 4 and 3) and 2,220 (digits 2 and 0) each have at least two different digits. (Kaprekar's steps, pages 62 and 63.)

Rules, guesses and estimates

Question 5. Rohan applies the Collatz rule starting at 103 and writes: 103, 309, ... Find his mistake and write the next four numbers correctly.

Answer: 103 is odd, so it becomes 3 × 103 + 1 = 310, not 309; then 155, 466, 233. For an odd number the rule is "multiply by 3 and add 1"; Rohan forgot to add 1. So: 103 → 310. 310 is even, so halve it: 155. 155 is odd: 3 × 155 + 1 = 466. 466 is even: 233. (The Collatz rule, pages 68 and 69.)

Question 6. A school bus has 46 seats and makes 9 full trips a day. Neha estimates that it carries about 4,500 children a day. Is her estimate sensible?

Answer: no; about 450 is sensible, so she is out by about ten times. 46 is close to 50, and 50 × 9 = 450, so the bus carries about 450 children a day (the exact number is 46 × 9 = 414). Neha's 4,500 is ten times too big, probably from writing an extra zero. (Estimation, page 69.)

Question 7. Is the sum of two 3-digit palindromes always a palindrome? Try 151 + 414 and 585 + 646.

Answer: only sometimes. 151 + 414 = 565, which is a palindrome. But 585 + 646 = 1,231, which reads 1,321 backwards, so it is not a palindrome. When no digits carry, each place adds matching digits and the sum stays a palindrome; a carry can break the pattern. One example that fails is enough to show it is not always true. (Palindromes, page 61.)

Question 8. Asha adds nine 97s quickly by writing 9 × 100 − 3 = 897. Find her mistake and give the correct total.

Answer: 873; she took away 3 only once. Each of the nine 97s is 3 less than 100, so the total is 9 × 100 − 9 × 3 = 900 − 27 = 873. (Adding numbers in a pattern a quicker way, page 67.)

Questions students ask

What is the Kaprekar constant? 6174. Starting from any 4-digit number with at least two different digits, and repeatedly subtracting the smallest number made from its digits from the largest, you always reach 6174. D.R. Kaprekar, a mathematics teacher in Devlali, Maharashtra, found this in 1949. (Pages 62 and 63.)

Is the Collatz conjecture proved? No. Lothar Collatz conjectured in 1937 that every Collatz sequence reaches 1, and it is still one of the most famous unsolved problems in mathematics. (Page 69.)

What is a palindromic number? A number that reads the same from left to right and from right to left, such as 4,554. (Page 61.)

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Sources

All opened and read on 22 October 2026. Page numbers are the printed page numbers of the textbook; printed page = PDF page + 54.

The facts are from the textbook pages above. The questions, worked answers and checks are our own, and every number was re-computed by script. This guide is general information; follow your teacher and the textbook.