Difference between revisions of "2007 USAMO Problems/Problem 4"
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== Problem == | == Problem == | ||
| + | An ''animal'' with <math>n</math> ''cells'' is a connected figure consisting of <math>n</math> equal-sized cells.<math>{}^1</math> The figure below shows an 8-cell animal. | ||
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| + | (insert picture here) | ||
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| + | 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. | ||
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| + | <math>{}^1</math>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 <math>n</math> cells, one with <math>n+1</math> cells is obtained by adjoining a new cell by making it adjacent to one or more existing cells. | ||
== Solution == | == Solution == | ||
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{{USAMO newbox|year=2007|num-b=3|num-a=5}} | {{USAMO newbox|year=2007|num-b=3|num-a=5}} | ||
Revision as of 18:05, 25 April 2007
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
| 2007 USAMO (Problems • Resources) | ||
| Preceded by Problem 3 |
Followed by Problem 5 | |
| 1 • 2 • 3 • 4 • 5 • 6 | ||
| All USAMO Problems and Solutions | ||
