Difference between revisions of "2018 IMO Problems/Problem 3"
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Does there exist an anti-Pascal triangle with <math>2018</math> rows which contains every integer from <math>1</math> to <math>1 + 2 + 3 + \dots + 2018</math>? | Does there exist an anti-Pascal triangle with <math>2018</math> rows which contains every integer from <math>1</math> to <math>1 + 2 + 3 + \dots + 2018</math>? | ||
== Solution == | == Solution == | ||
| + | penis | ||
Revision as of 18:08, 4 August 2018
An anti-Pascal triangle is an equilateral triangular array of numbers such that, except for the numbers in the bottom row, each number is the absolute value of the difference of the two numbers immediately below it. For example, the following is an anti-Pascal triangle with four rows which contains every integer from 
to 
![\[4\]](http://latex.artofproblemsolving.com/6/b/7/6b7cf66d599226c652df559a53d59485c0d579f3.png)
![\[2\quad 6\]](http://latex.artofproblemsolving.com/c/f/d/cfdaf528e2dab07f13bb71c8f883a5c50df18696.png)
![\[5\quad 7 \quad 1\]](http://latex.artofproblemsolving.com/d/e/7/de79303d7d5cc9d8ed468e01efcaa475fd6db6bb.png)
![\[8\quad 3 \quad 10 \quad 9\]](http://latex.artofproblemsolving.com/1/a/5/1a5f050424d37ee1537e46249b65b5bcb5e4033d.png)
Does there exist an anti-Pascal triangle with 
rows which contains every integer from to 
?
Solution
penis
