Anshu and his friends play the 'idli-vada' game with two numbers, which are both smaller than 10. The first time anybody says 'idli-vada' is after the number 50. What could the two numbers be which are assigned 'idli' and 'vada'?
Understanding: 'Idli-vada' is said for common multiples of the two numbers.
Condition: The first time 'idli-vada' is said is after 50, which means the LCM of the two numbers must be greater than 50.
Checking pairs smaller than 10: LCM(7, 8) = 56 LCM(7, 9) = 63 LCM(8, 9) = 72
Conclusion: The pairs (7, 8), (7, 9), and (8, 9) have their first common multiple after 50.
Answer: The two numbers could be 7 and 8, 7 and 9, or 8 and 9.
Explanation
'Idli-vada' is said for common multiples of the two numbers. The first time 'idli-vada' is said is after 50, which means the LCM of the two numbers must be greater than 50. For pairs smaller than 10: LCM(7,8)=56, LCM(7,9)=63, LCM(8,9)=72. The pairs (7,8), (7,9), and (8,9) have their first common multiple after 50.
Solution Steps
Step 1: We need two numbers less than 10 whose LCM is greater than 50.
Step 2: Check pair (6,9): LCM(6,9) = 18, which is not greater than 50, so this pair is invalid.
Step 3: Check pair (7,8): LCM(7,8) = 56, which is greater than 50.
Step 4: Check pair (7,9): LCM(7,9) = 63, which is greater than 50.
Step 5: Check pair (8,9): LCM(8,9) = 72, which is greater than 50.
Step 6: Possible pairs: (7,8), (7,9), (8,9).