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For The Mathematically Inclined

Anil Saigal
04/22/2021

Problem 1

What is the distance that the tip of a minute hand of a clock travels in 12 minutes, if the diameter of the clock is 30 cm and the hand extends to a distance of 2 cm from the edge of the clock?

Problem 2
A clock was set right at 6:00 AM. If it gains 3 1/2 minutes per hour, what time will it show at 6:00 PM on the same day? 

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Problems from M-04/08/21

Problem 1
PIN on Michael credit card is a four-digit number. Michael told this to his friend:
• It is a prime number - that is, a number greater than 1, which is only divisible by number one and by itself.
• The first digit is larger than the second.
• The second digit is greater than the third.
• The third digit is greater than 6.
• The fourth digit is odd.
• Three digits are odd.
What is Michael's PIN, if you know that five of the  above statements are true and one is false?


Problem 2
The Holiday Hotel has the same number of rooms on each floor. Rooms are numbered with natural numerals sequentially from the first floor, no number is omitted, and each room has a different number. Three tourists arrived at the hotel. The first one was in room number 50 on the fourth floor. The other room number 100 on the seventh floor, third in room number 126 on the ninth floor. How many rooms are on each floor?
 

Congratulations to Ramachandran Balakrishna, who was the winner of the last set of problems.



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