Find the Angle


triangle-puzzle Find the measure of angle "a" in the diagram.


This problem is known as Langley's Problem. It first appeared as 'A Problem', E M Langley, Mathematical Note 644, Mathematical Gazette, Volume 11, p. 173, 1922.


PDF Handout by Tom Rike (Berkeley Math Circle Handouts). An animated solution. Also see Adventitious Triangles and Langley type problems for an interesting discussion.

Previous Puzzle: Duplicate Integer

An array of length n+1 is populated with integers in the range [1, n]. Find a duplicate integer (just one, not all) in linear time with O(1) space. The array is read-only and may not be modified. Variation: what if the array may be written into but must be left unmodified by the algorithm?

Next Puzzle: Five Card Trick

A mathemagician asks a volunteer to give him five cards drawn from a pack of fifty-two. He hands one card back to the volunteer and arranges the remaining four in some sequence he chooses. He then hands the sequence to a second volunteer and leaves the room. His assistant enters. The assistant asks the second volunteer to read out aloud the sequence handed to him. The assistant ponders a little and correctly announces the identity of the card held by the first volunteer. How could this be done? In general, how large a deck of cards can be handled if n cards are drawn initially?

17 Aug 2011
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