- #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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