Tag Archives: Crux Mathematicorum

Passion Kiss Problem

This is a somewhat challenging math cryptogram in a slightly different guise from the Canadian Math Society’s magazine, Crux Mathematicorum.

“But you can’t make arithmetic out of passion. Passion has no square root.” (Steve Shagan, City of Angels, G.P. Putnam’s Sons, New York, 1975, p. 16.)

On the contrary, show that in the decimal system

has a unique solution.

See the Passion Kiss Problem

Twin Intersection Puzzle

This is an interesting problem from the 1977 Canadian Math Society’s magazine, Crux Mathematicorum.

“206. [1977: 10] Proposed by Dan Pedoe, University of Minnesota.

A circle intersects the sides BC, CA and AB of a triangle ABC in the pairs of points X, X’, Y, Y’ and Z, Z’ respectively. If the perpendiculars at X, Y and Z to the respective sides BC, CA and AB are concurrent at a point P, prove that the respective perpendiculars at X’, Y’ and Z’ to the sides BC, CA and AB are concurrent at a point P’.”

See the Twin Intersection Puzzle

Puzzles and Problems: plane geometry, Dan Pedoe, Crux Mathematicorum