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forum.virtualchallengemeets.com • View topic - USAMO 2007 Problem 4

USAMO 2007 Problem 4

Pose Olympiad-level questions to the monkeys in the peanut #.

USAMO 2007 Problem 4

Postby zefuri » Wed Apr 25, 2007 5:36 pm

An animal with [unparseable or potentially dangerous latex formula] cells is a connected figure consisting of [unparseable or potentially dangerous latex formula] equal-sized cells.1 The figure below shows an [unparseable or potentially dangerous latex formula]-cell animal.

(insert picture here)

A dinosaur is an animal with at least [unparseable or potentially dangerous latex formula] cells. It is said to be primitive it its cells cannot be partitioned into two or more dinosaurs. Find with proof the maximum number of cells in a primitive dinosaur.

1Animals are also called polyominoes. They can be defined inductively. Two cells are adjacent if they share a complete edge. A single cell is an animal, and given an animal with n cells, one with [unparseable or potentially dangerous latex formula] cells is obtained by adjoining a new cell by making it adjacent to one or more existing cells.
zefuri
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