Class 6 Chapter 3 Number Play Worksheet from NCERT Book

Let’s have a look at the worksheet that challenges students and prepares them for exams. We have covered the entire chapter while selecting the questions from each section. This will help Class 6 students thoroughly prepare for Chapter 3: Number Play.

Class 6 Mathematics Chapter 3 Number Play Worksheet

A. Numbers Can Tell Us Things (Taller Neighbours)

1. In a line, each child says the number of taller neighbours standing immediately next to them (left/right only).
   For 6 children of different heights, is it possible to get the sequence:
   1, 2, 2, 2, 2, 1?
   If yes, describe a possible height order (use H1 shortest … H6 tallest). If no, explain why.
2. For 5 children of different heights, can the sequence 2, 1, 1, 1, 2 ever happen?
   Give a clear reason.
3. With 7 children all of different heights, what is the maximum number of children who can say “2”?
   Also write one arrangement (shortest → tallest positions) that achieves it.

B. Supercells (Bigger than adjacent cells)

4. For the row: 420, 815, 600, 999, 100, 450, 449
   Mark all supercells and state how many supercells exist.
5. Create a row of 9 different 3-digit numbers (100–999) such that the number of supercells is as large as possible.
   Write the row and state the number of supercells you achieved.
6. Can a row of 8 different numbers have exactly 1 supercell?
   Either (a) construct an example or (b) prove it cannot happen.
7. Consider this 3×3 grid (neighbours are up/down/left/right only):
   312, 450, 275, 498, 367, 410, 120, 600, 305.
   List all supercells (write the numbers and their positions like (row, col)).
8. Fill a 3×3 grid using digits 1, 0, 6, 3, 9 (each number must be a 5-digit number using all these digits exactly once)
   such that only the centre cell is a supercell. (Any valid solution is fine.)

C. Patterns on the Number Line

9. Place these numbers in increasing order and then identify which two are closest:
   1050, 1500, 2180, 2754, 3050, 5030, 5300, 8400, 9590, 9950.
10. Without drawing, answer using reasoning:
    On a number line from 15,070 to 15,090, tick marks are at every 1 unit.
    If one point is at 15,077 and another at 15,083,
    how many integers lie strictly between them?

D. Playing with Digits

11. How many 4-digit numbers exist? How many 5-digit numbers exist?
    (Answer in numbers, not words.)
12. Digit sum challenge:
    (a) Find the smallest number whose digit sum is 14.
    (b) Find the largest 5-digit number whose digit sum is 14.
13. A 3-digit number has three consecutive digits (like 345).
    (a) Write all such 3-digit numbers possible.
    (b) Compute their digit sums and state the pattern you observe.
14. Digit detective:
    How many times does the digit 7 appear in the numbers from 1 to 200?
    Show a counting method; don’t list all numbers.

E. Pretty Palindromic Patterns

15. Using only digits 1, 2, 3, write all 4-digit palindromes possible.
16. A 5-digit palindrome is of the form A B C B A.
    If the number is odd and A = 2B and B = 2C, find the palindrome.
    (Digits must be valid 0–9.)
17. On a 12-hour clock, a time is palindromic if reading digits (ignoring “:”) gives a palindrome (example: 12:21).
    List all palindromic times between 1:00 and 12:59 that have two-digit minutes.

F. The Magic Number of Kaprekar

18. Perform the Kaprekar routine for 7421:
    form the largest number A from digits, form the smallest number B from digits,
    compute C = A − B, and repeat until you reach 6174.
    Write each round clearly and state how many rounds it took.
19. The chapter mentions that for many 3-digit numbers, the routine reaches a repeating loop.
    Start with 321 and perform the routine until you see repetition.
    What number begins repeating?

G. Games and Winning Strategies

20. Two players start at 0. On each turn, a player adds 1, 2, or 3.
    The player who first reaches 22 wins.
    (a) Is there a guaranteed winning strategy?
    (b) If yes, list the “safe numbers” the winning player should aim to say.

Class 6 Mathematics – Answer Key

Chapter: Number Play (NCERT) | Worksheet Answer Key (with reasoning)

A. Numbers Can Tell Us Things (Taller Neighbours)

1. Answer: Not possible.
   Reason: If a child says 2, both neighbours must be taller. Two adjacent children cannot both say 2.
   The sequence has adjacent 2’s, so it cannot happen.
2. Answer: Not possible.
   Reason: End children have only one neighbour, so the maximum they can say is 1. The sequence has 2 at both ends.
3. Answer: Maximum = 3 (positions 2, 4, 6).
   One example arrangement (shortest→tallest labels 1–7): 7, 1, 6, 2, 5, 3, 4
   (Then positions 2, 4, 6 each have two taller neighbours.)

B. Supercells (Bigger than adjacent cells)

4. Answer: Supercells are 815, 999, 450. Total = 3.
5. Answer: Maximum supercells in 9 cells = 5 (alternate high–low, including ends).
   Example row: 900, 100, 850, 150, 800, 200, 750, 250, 700
   Supercells: 900, 850, 800, 750, 700 → 5
6. Answer: Yes.
   Example: 1, 2, 3, 4, 5, 6, 7, 8
   Only the last cell is greater than its neighbour → exactly 1 supercell.
7. Answer: Supercells are:
   450 at (1,2), 498 at (2,1), 410 at (2,3), 600 at (3,2)
8. Answer: One valid grid (each number uses digits 1,0,6,3,9 exactly once) where only the centre is a supercell:

   Row 1: 10369    61930    10963
   Row 2: 63109    96310    61390
   Row 3: 13069    60931    13609

   Centre 96310 is larger than up/down/left/right; no other cell satisfies the condition.

C. Patterns on the Number Line

9. Answer (increasing order): 1050, 1500, 2180, 2754, 3050, 5030, 5300, 8400, 9590, 9950
   Closest pair: 5030 and 5300 (difference 270)
10. Answer: Integers strictly between 15077 and 15083 are 15078, 15079, 15080, 15081, 15082 → 5

D. Playing with Digits

11. Answer:
    4-digit numbers: 1000 to 9999 → 9000
    5-digit numbers: 10000 to 99999 → 90000
12. Answer:
    (a) Smallest number with digit sum 14: 59
    (b) Largest 5-digit number with digit sum 14: 95000
13. Answer:
    (a) 123, 234, 345, 456, 567, 678, 789
    (b) Digit sums: 6, 9, 12, 15, 18, 21, 24 → increases by 3 each time
14. Answer: 40
    Method: Ones place: 7, 17, …, 197 → 20 times. Tens place: 70–79 (10) and 170–179 (10) → 20 times. Total = 20 + 20 = 40.

E. Pretty Palindromic Patterns

15. Answer: 1111, 1221, 1331, 2112, 2222, 2332, 3113, 3223, 3333
16. Answer: No solution.
    Reason: A = 2B and B = 2C ⇒ A = 4C, so A is always even. But an odd palindrome needs the last digit A to be odd. Impossible.
17. Answer:
    1:01, 1:11, 1:21, 1:31, 1:41, 1:51
    2:02, 2:12, 2:22, 2:32, 2:42, 2:52
    3:03, 3:13, 3:23, 3:33, 3:43, 3:53
    4:04, 4:14, 4:24, 4:34, 4:44, 4:54
    5:05, 5:15, 5:25, 5:35, 5:45, 5:55
    6:06, 6:16, 6:26, 6:36, 6:46, 6:56
    7:07, 7:17, 7:27, 7:37, 7:47, 7:57
    8:08, 8:18, 8:28, 8:38, 8:48, 8:58
    9:09, 9:19, 9:29, 9:39, 9:49, 9:59
    10:01, 11:11, 12:21

F. The Magic Number of Kaprekar

18. Answer:
    7421 → 7421 − 1247 = 6174
    Reached in 1 round.
19. Answer: Repeating number is 495.
    Work: 321−123=198 → 981−189=792 → 972−279=693 → 963−369=594 → 954−459=495 (then repeats)

G. Games and Winning Strategies

20. Answer: Yes, there is a guaranteed winning strategy.
    Safe numbers: 2, 6, 10, 14, 18, 22
    Strategy: First say 2. After the opponent adds 1/2/3, respond by adding 3/2/1 so that the two moves total 4, landing on the next safe number.

Other Worksheets for Class 6

• Chapter 5 Prime Time Worksheet
• Chapter 6 Perimeter and Area Worksheet
• Chapter 7 Fractions Worksheet
• Chapter 10 The Other Side of Zero Worksheet