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.
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## Monthly Archives for August, 2013

## coin game

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"## Grid arrows

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?
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## Three spiders and a fly

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"