For The Mathematically Inclined

For The Mathematically Inclined

Anil Saigal
09/11/2014

Problem #1

I am in the habit of walking up the subway escalator while it is running. I climb 20 steps at my normal pace and it takes me 60 seconds to reach the top, whereas my wife climbs only 16 steps and it takes her 72 seconds to reach the top. If the escalator broke down tomorrow, how many steps would I have to climb?

Problem #2

How far is the horizon from the top of a 125.7-meter-high lighthouse? (The earth can be considered spherical with a circumference of 40,000 km.)

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Solutions from 8/28/2014

Problem #1

Alfred, Brian, Christopher and Damon play with a deck of 32 cards. Damon deals them out unequally, then says: "If you want us to have the same number of cards, do exactly as I say. You, Alfred, divide half of your cards between Brian and Christopher. Then, Brian, you do the same with Christopher and Alfred. Finally, Christopher, you follow suit with Alfred and Brian." How did Damon distribute the cards?

Problem #2

The product of three consecutive odd numbers is 357,627. What is the smallest of the three?

Congratulations to Saroj Gandhi, who was the winner of the last set of puzzles.

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