Grade 6 Prime Number: Idli-Vada Game

 

Idli-Vada Game

Children sit in a circle and play a game of numbers.
One of the children starts by saying '1'. The second player says '2', and so on. But when it is the turn of 3, 6, 9, ... (multiples of 3), the player should say 'idli' instead of the number. When it is the turn of 5, 10, ... (multiples of 5), the player should say 'vada' instead of the number. When a number is both a multiple of 3 and a multiple of 5, the player should say 'idli-vada'! If a player makes any mistake, they are out.
The game continues in rounds until only one player remains.
Here are the answers to the questions in the Idli-Vada Game:

🔢 Game Rules Summary

• Idli: Say for multiples of 3.
• Vada: Say for multiples of 5.
• Idli-Vada: Say for multiples of both 3 and 5.

Question 1
At what number is ‘idli-vada’ said for the 10th time?

• Explanation: 'Idli-vada' is said at every multiple of 15. The 10th time will be the 10th multiple of 15.
• Calculation: \(15 \times 10 = 150\)
• Answer: 150

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Question 2
If the game is played for the numbers 1 to 90, find out:
a. How many times would the children say ‘idli’ (including the times they say ‘idli-vada’)?
Calculation: \(90 \div 3 = 30\)
Answer: 30 times
b. How many times would the children say ‘vada’ (including the times they say ‘idli-vada’)?
Calculation: \(90 \div 5 = 18\)
Answer: 18 times
c. How many times would the children say ‘idli-vada’?
Calculation: \(90 \div 15 = 6\)
Answer: 6 times

Question 3
What if the game was played till 900? How would your answers change?

Answer: Each value from Question 2 increases exactly by 10 times:
Idli (multiples of 3): \(900 \div 3 = \mathbf{300\text{ times}}\)
Vada (multiples of 5): \(900 \div 5 = \mathbf{180\text{ times}}\)
Idli-Vada (multiples of 15): \(900 \div 15 = \mathbf{60\text{ times}}\)

Question 4
Is this figure somehow related to the ‘idli-vada’ game?
Answer: Yes. The overlapping circles (Venn Diagram) represent the groups of numbers:

• One circle contains multiples of 3 (Idli).
• The second circle contains multiples of 5 (Vada).
• The shared, overlapping middle section contains their common multiples (Idli-Vada), which are the multiples of 15 (e.g., 15, 30, 45, 60).