October 18, 2016
Problem of the Week
October 18, 2016
You are asked to join three match sticks end-to-end and to count how many distinct patterns you can form. No match stick is permitted to cross another and all three matches must be connected. Patterns are considered distinct only if there is no way to turn one match pattern into another without breaking or creating any new connections. By this definition the straight pattern shown below is considered the same as the Z pictured above it since the line can be turned into the Z by bending, spinning, and shifting. There are only three distinct match patterns for three matches. How many match patterns are there for four matches? Show each of the patterns that you find.
