For The Mathematically Inclined

For The Mathematically Inclined

Anil Saigal
08/17/2009

PROBLEM # 1
You are a cook in a remote area with no clocks or other way of keeping time other than a 4 minute hourglass and a 7 minute hourglass. You do have a stove however with water in a pot already boiling. Somebody asks you for a 9 minute egg, and you know this person is a perfectionist and will be able to tell if you undercook or overcook the eggs by even a few seconds. What is the least amount of time it will take to prepare the egg?

PROBLEM #2
The minute hand of a clock is twice as long as the hour hand. At what time, between 00:00 and when the hands are next aligned (just after 01:05), is the distance between the tips of the hands increasing at its greatest rate?

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Problem Solutions 08/06/09

PROBLEM # 1

A confused bank teller transposed the dollars and cents when he cashed a check for Ms. Smith, giving her dollars instead of cents and cents instead of dollars. After buying a newspaper for 50 cents, Ms Smith noticed that she had left exactly three times as much as the original check. What was the amount of the check?

Solution:

$18.56.

PROBLEM #2

What is the minimum number of times a fair die must be thrown for there to be at least an even chance that all scores appear at least once?

Solution:

Congratulations to Aseem Chandawarkar, Shailesh Goregaokar and Ranganath Nayak, who were the winner of the last set of puzzles.

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