Black or White
Professor Andy Liu
University of Alberta
Monday, October 9, 2017, 1:00 – 2:00 pm
608/5 1208/9 Mahavajirunnahit Building
Title 1: Symmetrix (material to be prepared in advance)
Our task is the construction symmetric figures, usually reflectional but sometimes rotational, from given sets of pieces. We focus our attention to puzzles with three pieces. For instant, one set consists of two isosceles triangles, with sides 5-5-6 and 5-5-8, and a scalene of Pythagorean fame, with sides 3-4-5. The mathematics underlying the design and solution of such puzzles will be discussed.
Title 2: Black or White
Our playing field is the standard 8 by 8 chessboard, with squares in alternating black and white pattern. One player thinks of a particular square on the chessboard, and the other player tries to discover the color of this square. To extract this information, the second player is allowed to fence off a simply connected part of the chessboard, and ask the first player whether the chosen square is inside or outside the region. What is the minimum number of questions the second player must ask to accomplish this task?