For The Mathematically Inclined

For The Mathematically Inclined

Anil Saigal
03/10/2015

Problem #1

M My daughter is twice as old as my son and half as old as I am. In twenty-two years my son will be half my age. How old is my daughter?

Problem #2

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?

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Solutions from 02/26/2015

Problem #1

What is the smallest integer greater than 0 that can be written entirely with zeros and ones and is evenly divisible by 225?
Solution:

Problem #2

Assuming the earth earth is spherical with radius r. What is the shortest distance along the surface from point A to point B. Let p1 and p2 be the two longitudes, measured from 0 to 2*pi. Let q1 and q2 be the two latitudes, measured from 0 to pi, where 0=north pole and pi=south pole.

Solution:

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