Difference between revisions of "2023 SSMO Relay Round 3 Problems/Problem 3"
(Created page with "==Problem== Let <math>T=</math> TNYWR. Let <math>n = N+1.</math> A spray painter has a paint gun that paints all areas within a radius of <math>2.</math> The spray painter wal...") |
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Latest revision as of 22:29, 15 December 2023
Problem
Let 
TNYWR. Let 
A spray painter has a paint gun that paints all areas within a radius of 
The spray painter walks in the following locations, where red lines indicate red paint coming out of the gun and blue lines indicate blue paint coming out of the gun. The spray painter starts from the outermost square and works his way inwards, where in the end. The positive difference between the area of the blue-painted region and the area of the red-painted region is 
Find 
(Note: if a spray painter paints an area with multiple colors, only the last color will be showing).
![[asy] unitsize(7mm); label("(1,1)",(1,1.5)); label("(-1,1)",(-1,1.5)); label("(-1,-1)",(-1,-1.5)); label("(1,-1)",(1,-1.5)); label("(2,2)",(2,2.5)); label("(-2,2)",(-2,2.5)); label("(-2,-2)",(-2,-2.5)); label("(2,-2)",(2,-2.5)); label("(3,3)",(3,3.5)); label("(-3,3)",(-3,3.5)); label("(-3,-3)",(-3,-3.5)); label("(3,-3)",(3,-3.5)); label("(N,N)",(9,9.5)); label("(-N,-N)",(-9,-9.5)); label("(-N,N)",(-9,9.5)); label("(N,-N)",(9,-9.5)); label("(N-1,N-1)",(7.3,8.5)); label("(-N+1,-N+1)",(-7.3,-8.5)); label("(-N+1,N-1)",(-7.3,8.5)); label("(N-1,-N+1)",(7.3,-8.5)); label("(N-2,N-2)",(5.5,7.5)); label("(-N+2,N+2)",(-5.5,-7.5)); label("(-N+2,N-2)",(-5.5,7.5)); label("(N-2,-N+2)",(5.5,-7.5)); draw((1,1)--(-1,1)--(-1,-1)--(1,-1)--cycle,red); draw((2,2)--(-2,2)--(-2,-2)--(2,-2)--cycle,blue); draw((3,3)--(-3,3)--(-3,-3)--(3,-3)--cycle,red); draw((7,7)--(-7,7)--(-7,-7)--(7,-7)--cycle,red); draw((8,8)--(-8,8)--(-8,-8)--(8,-8)--cycle,blue); draw((9,9)--(-9,9)--(-9,-9)--(9,-9)--cycle,red); dot((1,1),red); dot((-1,1),red); dot((1,-1),red); dot((-1,-1),red); dot((2,2),blue); dot((-2,2),blue); dot((2,-2),blue); dot((-2,-2),blue); dot((3,3),red); dot((-3,3),red); dot((3,-3),red); dot((-3,-3),red); dot((7,7),red); dot((-7,7),red); dot((7,-7),red); dot((-7,-7),red); dot((8,8),blue); dot((-8,8),blue); dot((8,-8),blue); dot((-8,-8),blue); dot((9,9),red); dot((-9,9),red); dot((9,-9),red); dot((-9,-9),red); dot((0,4)); dot((0,-4)); dot((4,0)); dot((-4,0)); dot((0,5)); dot((0,-5)); dot((5,0)); dot((-5,0)); dot((0,6)); dot((0,-6)); dot((6,0)); dot((-6,0)); [/asy]](http://latex.artofproblemsolving.com/b/a/c/bacde787969eb3c7d271531c03b201f1a9a279d2.png)
