2007 USAMO Problems/Problem 4
Problem
An animal with cells is a connected figure consisting of
equal-sized cells.
The figure below shows an 8-cell animal.
(insert picture here)
A dinosaur is an animal with at least 2007 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.
Animals 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
cells, one with
cells is obtained by adjoining a new cell by making it adjacent to one or more existing cells.
Solution
The answer is 4*(2007-1)+1=8025.
2007 USAMO (Problems • Resources) | ||
Preceded by Problem 3 |
Followed by Problem 5 | |
1 • 2 • 3 • 4 • 5 • 6 | ||
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