Class 7 Maths · Original EZT practice
Number Play (Class 7 Chapter 6): summary and practice
Odd or even, patterns in a grid, a sequence that appears in petals and spirals. Chapter 6 uses number puzzles to practise reasoning. All questions are original EZT tutor practice following the chapter's own section order. Edition note: this page covers the new NCERT book Ganita Prakash (Grade 7). Older Class 7 books had no chapter with this name - check your chapter title, not just the number.
8 original worked examples, 8 fresh self-check questions and 4 mixed questions, with explained answers. These are not copied textbook exercises, an official chapter index or a full answer key. No affiliation with NCERT is claimed.
Official sources for topic and edition context, checked 20 October 2026:
1. Numbers tell us things
A number can be read for information: its size, whether it is odd or even, what it is divisible by. Looking for such clues is the first step in solving a number puzzle.
2. Picking parity
Parity means odd or even. Even plus even is even; odd plus odd is even; even plus odd is odd. A product is even whenever any factor is even.
3. Explorations in grids
In a number grid, rows, columns and diagonals can hide patterns, such as sums that stay constant or grow by a fixed step. Spot the pattern, then test it on more cells.
4. The Virahanka-Fibonacci sequence
Start with one and two and add the last two terms to get the next: one, two, three, five, eight, thirteen. Virahanka described it in India for counting rhythms of long and short beats, centuries before Fibonacci. The same pattern appears in petals and spirals.
5. Digits in disguise
In cryptarithms, letters stand for digits. Work from the units column first, track the carry, and remember that a digit cannot be reused for a different letter.
Choose, solve, check, then try a fresh question.
Before calculating, read the method prompt and name the condition that makes it useful. Write your own attempt. Open the steps only when you need them, and use the check to catch a wrong sign, unit or interpretation. Finish with the fresh question before reading its answer.
Tell odd from even by the units digit
Choose the method: Look only at the units digit.
EZT practice question
Is four thousand six hundred eighty-three odd or even, and why?
Show the worked solution
- The units digit is three.
- Three is odd.
Answer: Odd - the units digit three is odd.
Check: A number's parity is decided by its last digit alone.
Watch for this: Do not add all the digits; parity needs only the units digit.
Now try it yourself
Is seven thousand two hundred forty even?
Check your answer
Yes - its units digit zero is even.
Zero is an even digit.
Check divisibility by nine
Choose the method: Add the digits; a digit sum of nine means divisible by nine.
EZT practice question
Which of thirty-six, forty-five and fifty-two is divisible by nine?
Show the worked solution
- The digit sums are nine, nine and seven.
- A digit sum of nine means the number is divisible by nine.
Answer: Thirty-six and forty-five - their digit sums are both nine.
Check: Thirty-six is four nines and forty-five is five nines.
Watch for this: Do not test the last digit; nine has no last-digit rule.
Now try it yourself
Is sixty-three divisible by nine?
Check your answer
Yes - six plus three is nine.
The digit sum is nine.
Track parity through a sum
Choose the method: Add parities step by step instead of computing the full sum.
EZT practice question
Is seventeen plus twenty-four plus nine odd or even?
Show the worked solution
- Seventeen plus twenty-four is forty-one, which is odd.
- Forty-one plus nine is fifty, which is even.
Answer: Even - the running total ends at fifty.
Check: Odd plus even is odd; odd plus odd is even.
Watch for this: Do not decide from the last addend alone; track every step.
Now try it yourself
What is the parity of six times thirteen times seven?
Check your answer
Even - the factor six is even.
A product with any even factor is even.
Use parity to prove impossibility
Choose the method: Count how many odd numbers are being added.
EZT practice question
Can five odd numbers add up to twenty?
Show the worked solution
- Each pair of odds gives an even sum.
- Four odds make two even pairs, and the fifth odd makes the total odd.
Answer: No - five odd numbers always give an odd sum, and twenty is even.
Check: An odd count of odd addends gives an odd total.
Watch for this: Do not hunt for examples; the parity argument settles it at once.
Now try it yourself
Can three odd numbers sum to thirty-one?
Check your answer
Yes - three odds make an odd total, for example nine plus eleven plus eleven.
Thirty-one is odd, so an odd count of odds can reach it.
Link a consecutive sum to its middle number
Choose the method: Compare the sum of three consecutive numbers with the middle one.
EZT practice question
In a calendar grid, four plus five plus six is fifteen and eleven plus twelve plus thirteen is thirty-six. What links the sum of three consecutive numbers to the middle one?
Show the worked solution
- Fifteen is three times five.
- Thirty-six is three times twelve.
Answer: The sum equals three times the middle number.
Check: The neighbours sit one below and one above the middle, so they average to it.
Watch for this: Do not assume the rule works only for these two examples; test any triple.
Now try it yourself
What is the middle number when three consecutive numbers sum to one hundred eleven?
Check your answer
Thirty-seven.
One hundred eleven divided by three is thirty-seven.
Find three consecutive numbers from their sum
Choose the method: Divide the sum by three to get the middle number.
EZT practice question
Three consecutive numbers sum to fifty-one. Find them.
Show the worked solution
- Fifty-one divided by three is seventeen.
- The middle number is seventeen.
Answer: Sixteen, seventeen and eighteen.
Check: Sixteen plus seventeen plus eighteen is fifty-one.
Watch for this: Do not take seventeen as the first number; it is the middle one.
Now try it yourself
Consecutive numbers sum to sixty - find them.
Check your answer
Nineteen, twenty and twenty-one.
Sixty divided by three is twenty, the middle number.
Continue the Virahanka-Fibonacci sequence
Choose the method: Each term is the sum of the two before it.
EZT practice question
Continue one, two, three, five, eight, thirteen by three more terms.
Show the worked solution
- Eight plus thirteen is twenty-one.
- Thirteen plus twenty-one is thirty-four.
- Twenty-one plus thirty-four is fifty-five.
Answer: Twenty-one, thirty-four and fifty-five.
Check: Each new term equals the sum of the previous two.
Watch for this: Do not add the last term to itself; use the last two different terms.
Now try it yourself
What are the next two terms after eight, thirteen, twenty-one, thirty-four?
Check your answer
Fifty-five and eighty-nine.
Twenty-one plus thirty-four is fifty-five; thirty-four plus fifty-five is eighty-nine.
Solve a two-digit cryptarithm
Choose the method: Start at the units column, then carry into the tens.
EZT practice question
In A three plus four B equals ninety, A and B are single digits. Find them.
Show the worked solution
- Units: three plus B ends in zero, so B is seven with a carry of one.
- Tens: A plus four plus the carry of one equals nine, so A is four.
Answer: A is four and B is seven - forty-three plus forty-seven is ninety.
Check: Forty-three plus forty-seven equals ninety.
Watch for this: Do not forget the carry from the units column when solving the tens.
Now try it yourself
B plus B equals eighteen - find B.
Check your answer
Nine.
Nine plus nine is eighteen.
Try a mixed set
Choose a method or explanation before opening each answer.
1. What is parity?
Show answer and reason
Whether a number is odd or even.
Parity rules predict sums and products without full calculation.
2. What is the digit-sum test for nine?
Show answer and reason
If the digits add to a multiple of nine, the number is divisible by nine.
The digit sum keeps the remainder on division by nine.
3. What rule builds the Virahanka-Fibonacci sequence?
Show answer and reason
Each term is the sum of the two terms before it.
Starting from one and two gives one, two, three, five, eight.
4. Where do you start a cryptarithm?
Show answer and reason
At the units column, tracking carries.
The units column has the fewest unknowns.
Try it yourself
Work these on paper before checking any notes. Answers are deliberately not shown here.
- Is ninety-one thousand four hundred six divisible by nine? Use the digit-sum test.
- Can seven odd numbers add up to one hundred? Explain using parity.
- In C four plus two D equals seventy, find the digits C and D.
Know the rule but lose track of the steps?
Bring your book edition, your school topic list and a question you attempted. Ask a tutor to explain the choice of method and test it with a different problem. Agree the lesson topics, schedule and fee before starting.
For cost context, see home tuition fees in Delhi NCR. Agree the topics, schedule and fee with your chosen tutor.
Questions about this practice page
- What is parity?
- Whether a number is odd or even.
- Can five odd numbers add to an even number?
- No - five odd numbers always give an odd sum.
- What is the Virahanka-Fibonacci sequence?
- One, two, three, five, eight, thirteen and so on, where each term is the sum of the two before it.
- How do you solve a digit puzzle?
- Start at the units column, track carries, and keep different letters as different digits.
- Are these the NCERT exercise questions for Number Play (Class 7)?
- No. EZT pages are original practice following the chapter's section order - use them to prepare for the textbook exercises, not as a substitute for your book.