CBSE Math Revision Start revising
Themed maths · 14 November

Children’s Day maths puzzle challenge for CBSE Class 9 and 10

A ready-to-run puzzle challenge for Children’s Day on 14 November: a 5-minute warm-up, four 8–9 minute rounds (number, algebra, geometry and chance) for teams, a bonus round and full worked answers. No calculator.

Level
CBSE Class 9 and 10
Time
40 minutes, plus a 10-minute extension
Topics
Real numbers: HCF, LCM and remainders; Pair of linear equations; Quadratic equations; Triangles, angles and quadrilaterals; Probability
Equipment
No calculator. Every answer works out exactly.

Download student sheet (PDF)Answers (PDF)

Suggested timings

PartTimeWhat
Starter5 minQuick questions on the board
Main: task A9 minNumber round
Main: task B9 minAlgebra round
Main: task C9 minGeometry round
Main: task D8 minChance round
Extension10 minFast finishers or homework

Starter (5 minutes)

Warm-up: answer on mini whiteboards.

  1. Today is 14/11. Work out 14 × 11 in your head.
  2. A number is doubled and then 7 is added. The result is 35. What was the number?
  3. What is the sum of the interior angles of a hexagon?
  4. How many prime numbers are there between 1 and 30?

Main activity (35 minutes)

Task A: Number round (9 min)

Teams work together; one answer per team.

  1. Find the smallest positive whole number that leaves remainder 1 when divided by 2, 3, 4, 5 or 6, and is exactly divisible by 7.
  2. The HCF of two numbers is 11 and their LCM is 154. One of the numbers is 22. Find the other.
  3. What is the last digit of 714?

Task B: Algebra round (9 min)

Set up an equation for each puzzle.

  1. A father is 4 times as old as his daughter. In 14 years he will be twice as old as her. How old are they now?
  2. The sum of a positive number and its reciprocal is 10/3. Find the number (two answers).
  3. 3 pens and 2 notebooks cost ₹110. 2 pens and 3 notebooks cost ₹115. Find the cost of one pen and one notebook.

Task C: Geometry round (9 min)

Draw a sketch first.

  1. A right-angled triangle has shorter sides 9 cm and 12 cm. Find its hypotenuse and its area.
  2. The angles of a quadrilateral are in the ratio 3 : 4 : 5 : 6. Find the largest angle.
  3. What is the angle between the hour and minute hands of a clock at 3:30?

Task D: Chance round (8 min)

Write each answer as a fraction in its lowest terms.

  1. Two dice are thrown. Find the probability that the total is 7.
  2. A card is picked at random from cards numbered 1 to 50. Find the probability that the number is a multiple of 4 or of 6.
  3. A coin is tossed three times. Find the probability of at least two heads.

Extension (10 minutes)

Bonus round for the fastest teams.

  1. How many squares of all sizes are there on an 8 by 8 chessboard?
  2. The sum of three consecutive odd numbers is 147. Find the numbers.

For teachers

Teacher notes and full worked answers
  • Run it as a team quiz: teams of three or four, one answer sheet per team, one mark per correct answer, and 1 extra mark for clear working in the algebra round.
  • The rounds are independent, so you can use one round as a starter on another day.
  • In the number round, the clock and last-digit questions reward spotting a repeating pattern: ask teams to explain how they found it.

Starter

  1. 154
    • 14 × 11 = 140 + 14 = 154
  2. 14
    • 2x + 7 = 35, so 2x = 28 and x = 14.
  3. 720°
    • (6 − 2) × 180° = 720°
  4. 10
    • 2, 3, 5, 7, 11, 13, 17, 19, 23, 29

Task A: Number round

  1. 301
    • Remainder 1 when divided by 2, 3, 4, 5 and 6 means one more than a multiple of LCM(2, 3, 4, 5, 6) = 60.
    • Try 61, 121, 181, 241, 301: the first multiple of 7 is 301 = 7 × 43.
  2. 77
    • HCF × LCM = product of the numbers: 11 × 154 = 1694.
    • 1694 ÷ 22 = 77
  3. 9
    • The last digits of 7, 72, 73, 74 are 7, 9, 3, 1, and then the pattern repeats every 4.
    • 14 = 4 × 3 + 2, so the last digit is the same as for 72: 9.

Task B: Algebra round

  1. Daughter 7, father 28
    • Let the daughter be x: 4x + 14 = 2(x + 14).
    • 4x + 14 = 2x + 28, so 2x = 14 and x = 7. The father is 28.
  2. 3 or 1/3
    • x + 1/x = 10/3 gives 3x2 − 10x + 3 = 0.
    • (3x − 1)(x − 3) = 0, so x = 3 or 1/3.
  3. Pen ₹20, notebook ₹25
    • Add the equations: 5p + 5n = 225, so p + n = 45.
    • Subtract them: p − n = −5.
    • So 2p = 40: p = 20 and n = 25.

Task C: Geometry round

  1. 15 cm; 54 cm2
    • √(81 + 144) = √225 = 15
    • Area = ½ × 9 × 12 = 54
  2. 120°
    • 3 + 4 + 5 + 6 = 18 parts = 360°, so 1 part = 20°.
    • Largest = 6 × 20° = 120°
  3. 75°
    • The minute hand points at 6: 180° from 12.
    • The hour hand is halfway from 3 to 4: 90° + 15° = 105° from 12.
    • 180° − 105° = 75°

Task D: Chance round

  1. 1/6
    • (1, 6), (2, 5), (3, 4), (4, 3), (5, 2), (6, 1): 6 of the 36 outcomes.
    • 6/36 = 1/6
  2. 8/25
    • Multiples of 4: 12. Multiples of 6: 8. Multiples of both (of 12): 4.
    • 12 + 8 − 4 = 16, so 16/50 = 8/25.
  3. 1/2
    • HHH, HHT, HTH, THH: 4 of the 8 outcomes.
    • 4/8 = 1/2

Extension

  1. 204
    • There are 82 squares of size 1 by 1, 72 of size 2 by 2, and so on down to 12 of size 8 by 8.
    • 64 + 49 + 36 + 25 + 16 + 9 + 4 + 1 = 204
  2. 47, 49, 51
    • (x − 2) + x + (x + 2) = 3x = 147, so x = 49.

The same answers are in the answers PDF. Every answer was recomputed by computer before publishing.

Practise the topics

Fibonacci Day maths · National Mathematics Day maths · Women in maths maths · All themed maths

More for lessons: Weekly starters · Worksheet builder · Olympiad and competition maths · National Mathematics Day puzzles