- #1
CantorSet
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Hi everyone,
For fun, I decided to check out some problems from a math competition designed for advanced high school students. I came across this problem that I can't seem to figure out. The contestants are suppose to be able to get it in 3 minutes (it's part of a 20 question test given in an hour). It's a multiple choice problem:
18) Let [itex]N = 10^{2000}+2000[/itex] , and let S be the set of consecutive integers from 1 to N. In how many different ways can three consecutive integers be removed from S so that the average of the remaining numbers is an integer?
A) 1
B) 2
C) 3
D) 4
E) 6
Here is the link to the original problem. It's number 18.
http://webserver.forest.org.uk/resource.aspx?id=27123
For fun, I decided to check out some problems from a math competition designed for advanced high school students. I came across this problem that I can't seem to figure out. The contestants are suppose to be able to get it in 3 minutes (it's part of a 20 question test given in an hour). It's a multiple choice problem:
18) Let [itex]N = 10^{2000}+2000[/itex] , and let S be the set of consecutive integers from 1 to N. In how many different ways can three consecutive integers be removed from S so that the average of the remaining numbers is an integer?
A) 1
B) 2
C) 3
D) 4
E) 6
Here is the link to the original problem. It's number 18.
http://webserver.forest.org.uk/resource.aspx?id=27123
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