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10/16/2007

March 2–March 8, 2010

Problem

A square grid of side 4398046511104 has it left-top corner removed. Is it possible to fill this new grid with pieces of the form

an 'L' triomino

(rotations of the pieces are allowed) without overlapping such pieces?

Solution

Many people used an induction argument together with the fact that 4398046511104 = 2⁴² to prove the theorem. Here is an alternate approach.

List of solvers

David Lingenbrink (high school); Kazuo Thow, Daniel Nollette (undergrad); Jack Lee (faculty); Michael Duncan, Shreevatsa R, Lawrence Hon, Lloyd Sakazaki, Peiyush Jain, Congpa You, Brett K., Brad Heller (outside).

David Lingenbrink wins the prize!