MathDB

10

Part of 2003 Austrian-Polish Competition

Problems(1)

smallest no of 5x1 tiles which must be placed on a 31x5 rectangle

Source: Austrian Polish 2003 APMC

4/25/2020
What is the smallest number of 5×15\times 1 tiles which must be placed on a 31×531\times 5 rectangle (each covering exactly 55 unit squares) so that no further tiles can be placed? How many different ways are there of placing the minimal number (so that further tiles are blocked)? What are the answers for a 52×552\times 5 rectangle?
geometryrectangle