For The Mathematically Inclined

For The Mathematically Inclined

Anil Saigal
08/25/2009

PROBLEM # 1
What number is 1/3 orf the way from 1/4 to 4/3?

PROBLEM #2
One dimension of the cube is increased by 1, another one is decreased by 1, and the third is left unchanged. The volume of the new rectangular solid is 5less yhan that of the cube. What was the volume of the cube?

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Problems from 08/20/09

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?

Congratulations to Roopesh Mathur, who was the winner of the last set of puzzles.

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