Number Play Class 6 Worksheet — Free PDF Download with Answers

Number Play is one of the most engaging chapters in the Class 6 NCERT Ganita Prakash textbook. It invites students to explore numbers not as dry symbols on a page but as living objects with surprising properties. Why does reversing and subtracting a two-digit number always give a multiple of $9$? Why are palindromes special? What makes magic squares magical?

This chapter covers divisibility rules, digit sums, palindromic numbers, number puzzles, and magic squares. It also introduces the idea that mathematics is about exploration and reasoning, not just computation. Students who enjoy this chapter often develop a lasting appreciation for mathematical thinking.

While ICSE and IB do not have a chapter titled "Number Play," many of the underlying ideas — divisibility, digit properties, logical reasoning — appear across their syllabi. This worksheet is therefore useful for students of all boards who want to sharpen their number sense and logical thinking.

Refresh these ideas before the worksheet:

* Divisibility rules:
- By $2$: last digit is even.
- By $3$: sum of digits is divisible by $3$.
- By $4$: last two digits form a number divisible by $4$.
- By $5$: last digit is $0$ or $5$.
- By $9$: sum of digits is divisible by $9$.
- By $11$: alternating sum of digits is $0$ or divisible by $11$.
* Digit sum — Add all digits of a number. E.g., digit sum of $487 = 4 + 8 + 7 = 19 \to 1 + 9 = 10 \to 1 + 0 = 1$.
* Palindromic numbers — Read the same forwards and backwards: $121, 1331, 14641$.
* Reverse and subtract trick — For any two-digit number $\overline{ab}$ where $a > b$: $\overline{ab} - \overline{ba}$ is always a multiple of $9$.
* Magic squares — An $n \times n$ grid where every row, column, and diagonal sums to the same number (the magic constant).
*Magic constant for a $3 \times 3$ magic square** using $1$ to $9$: $\dfrac{n(n^2 + 1)}{2} = \dfrac{3 \times 10}{2} = 15$.

1. Print the PDF — Download from the links below and work with pencil and paper.

2. Start with Level 1 (Easy) — 20 questions on divisibility tests, digit sums, and identifying palindromes.

3. Time yourself — 15 minutes for Level 1, 20 for Level 2, 25 for Level 3.

4. Check answers — Use the answer key provided in the PDF.

5. Revise mistakes — For puzzle questions, trace through the logic step by step to find where you went wrong.

6. Move to the next level — Progress when you score 16/20 or above.

Level 1 — Easy

1. Is $4{,}572$ divisible by $3$? Check using the digit-sum rule.
Solution: $4 + 5 + 7 + 2 = 18$. Since $18$ is divisible by $3$, yes, $4{,}572$ is divisible by $3$.

2. Write the smallest 4-digit palindrome.
Solution: $1{,}001$.

3. What is the digit sum of $9{,}999$?
Solution: $9 + 9 + 9 + 9 = 36 \to 3 + 6 = 9$.

Level 2 — Medium

1. Take the number $73$. Reverse it to get $37$. Find $73 - 37$. Is it a multiple of $9$?
Solution: $73 - 37 = 36 = 9 \times 4$. Yes.

2. Complete the magic square where the magic constant is $15$:
$\begin{array}{|c|c|c|} \hline 2 & ? & 6 \\ \hline ? & 5 & ? \\ \hline ? & ? & ? \\ \hline \end{array}$
Solution: Row 1: $2 + ? + 6 = 15 \Rightarrow ? = 7$. Middle row has $5$, so the square is the standard $3 \times 3$ magic square rearranged: $\begin{array}{|c|c|c|} \hline 2 & 7 & 6 \\ \hline 9 & 5 & 1 \\ \hline 4 & 3 & 8 \\ \hline \end{array}$.

3. Find the largest 5-digit number divisible by both $5$ and $9$.
Solution: Divisible by $5$: ends in $0$ or $5$. Divisible by $9$: digit sum divisible by $9$. Largest 5-digit number $= 99{,}999$. Check: $9+9+9+9+9 = 45$ (divisible by $9$), ends in $9$ (not $0$ or $5$). Try $99{,}990$: digit sum $= 45$, ends in $0$. Answer: $99{,}990$.

Level 3 — Hard

1. Prove that $\overline{ab} - \overline{ba} = 9(a - b)$ for a two-digit number where $a > b$.
Solution: $\overline{ab} = 10a + b$ and $\overline{ba} = 10b + a$. So $\overline{ab} - \overline{ba} = (10a + b) - (10b + a) = 9a - 9b = 9(a - b)$.

2. A $4 \times 4$ magic square uses numbers $1$ to $16$. What is its magic constant?
Solution: Sum of $1$ to $16$ is $\frac{16 \times 17}{2} = 136$. Magic constant $= \frac{136}{4} = 34$.

3. Find a 3-digit number that equals the sum of the cubes of its digits.
Solution: $153 = 1^3 + 5^3 + 3^3 = 1 + 125 + 27 = 153$. (This is called a narcissistic number.)

CBSE (NCERT — Ganita Prakash)
Ganita Prakash dedicates a full chapter to "Number Play," covering divisibility tricks, palindromes, magic squares, and number puzzles. The chapter encourages exploration and discovery. CBSE exam questions test divisibility rules, digit sums, and puzzle completion.

ICSE (Selina / ML Aggarwal)
ICSE does not have a standalone Number Play chapter. However, divisibility rules are covered in the Number System chapter, and number puzzles appear in Mental Maths sections. ICSE students benefit from this worksheet as supplementary enrichment material.

IB MYP (Mathematics Framework)
The MYP framework embeds number exploration within its Number unit. Students investigate properties of numbers through inquiry tasks. Magic squares and palindromes may appear as extension activities. The investigative mindset aligns well with this worksheet's Level 3 questions.

Key Differences:
* CBSE: Full dedicated chapter with hands-on exploration.
* ICSE: Divisibility covered formally; puzzles as enrichment.
* IB: Inquiry-based; puzzles as investigation tasks.

Download your free Number Play worksheet:

* Number Play CBSE Worksheet — 60 questions aligned to Ganita Prakash

Practise interactively online:

* Practice Online — CBSE

Each worksheet has 20 questions per level with a detailed answer key.

* AI Maths Solver — Stuck on a number puzzle? Get a step-by-step solution.
* Spark Coach — AI tutor that gives hints to help you crack puzzles yourself.
* Free Worksheets for All Classes — Browse worksheets across all classes and boards.
* Play Mode for Class 1-4 — Game-based number activities for younger learners.

Continue exploring Class 6 maths:

* Numbers & Place Value Class 6 Worksheet
* Whole Numbers Class 6 Worksheet
* Patterns in Mathematics Class 6 Worksheet
* Prime Numbers & Factors Class 6 Worksheet
* Integers Class 6 Worksheet