Gurmeet.Net
Puzzles

## Find the Angle

### Puzzle

Find the measure of angle "a" in the diagram.

### Source

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.

### Solution

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?