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For The Mathematically Inclined

Anil Saigal
04/07/2021

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?


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Problems from M-03/25/21

Problem 1:
The greater part of the earth's surface (r = 6371 km) is covered by oceans; their area is approximately 71% of the Earth's surface. What is the approximate area of the land?

Problem 2:
What is  the surface area of the cylinder when its volume is 45 liters and the perimeter of base is three times of the height?
 

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



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