Puzzles
A geometry problem so simple it took a year to solve properly
Draw an isosceles triangle with its two base angles at 80°. From one corner, a line at 30° cuts across to the opposite side; from the other corner, a line at 20° does the same. Using nothing but a ruler's worth of given angles, find the angle where those two new lines cross.
Reveal the answer
30°. Edward Langley posed this in 1922 expecting an elegant solution using only classical straightedge-and-compass angle-chasing, but no such proof appeared until James Mercer found one in 1923, needing one extra construction line. It's still called 'the hardest easy geometry problem'.
— Edward Mann Langley, A Problem — The Mathematical Gazette, 1922