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Monthly Archives for August, 2013

Projector illumination

Posted on: August 21st, 2013 by

A projector in 2D space can illuminate a quadrant of the plane (it's field of vision is 90 degrees). Show that 4 projectors at 4 arbitrary points can be rotated so as to illuminate the entire plane. via Math Puzzles

coin game

Posted on: August 20th, 2013 by

There is a bag containing an unlimited number of identical coins. You and your friend want to play the following game: Each player takes turns placing a coin on the table such that the coin doesn't overlap with any other coin. The first player who is unable to place a new coin on a table loses. If you are playing first what is your winning Continue reading the story "coin game"

Optimal solution

Posted on: August 19th, 2013 by

You are in a car at a bus stop. 3 people are stranded at the stop: an old granny, your best friend and your lover. However, your car is a 2 seater. How would you help all 3 people who are stranded? - via Uma Suri

Tetrahedron faces

Posted on: August 18th, 2013 by
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Prove that if all 4 faces of a tetrahedron are of the same area, they are equal. - via Russian math Olympiad.


Posted on: August 17th, 2013 by

One number among 1 to 15 and 99 others from 1 to 200 are chosen. Show that there are two chosen numbers such that one divides the other.

Acute angles

Posted on: August 16th, 2013 by

What is the largest number of acute angles that a convex polygon can have? - Russian math olympiad


Posted on: August 15th, 2013 by


An inequality

Posted on: August 14th, 2013 by

Suppose a_2,a_3,\dots a_n are positive reals such that \prod_{i=2}^na_i=1. Show that (1+a_2)^2(1+a_3)^3\dots(1+a_n)^n\geq n^n - via Packard white board at Stanford

Grid arrows

Posted on: August 13th, 2013 by

There is an infinite checkerboard. Each square contains an arrow in one of the eight directions: North, North-east, .... Two squares with a common edge cannot have arrows differing by more than 45 degrees. Suppose you start at some square, move to the next square pointed to by the arrow, and so on. Can you find a closed cycle? - Via Math puzzles

Three spiders and a fly

Posted on: August 12th, 2013 by

Three spiders and a fly are constrained to move on the edges of a regular tetrahedron. The fly can travel at the maximum speed of 1 edge per sec whereas each spider can travel at 1+epsilon edges/sec. The fly is invisible to the spiders and the fly has perfect knowledge of the locations and strategy of the spiders. Can the spiders agree on a strategy Continue reading the story "Three spiders and a fly"

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