Posted by keshav on .
The integers from 1 through 10 (inclusive) are divided into three groups, each containing at least one number. These groups satisfy the additional property that if x is in a group and 2x≤10, then 2x is in the same group. How many different ways are there to create the groups?

maths 
Shame,
Shame on you Keshav!!! Cheating on Brilliant!!! This site is meant to be a platform to practice your own skills, not to copy paste the questions and get free answers and then get incentives without effort. So either play fair and be honest or leave this site. People like you are shame to the Brilliant community. And to the others, please give the answer to this problem after Monday 10/6/2013, so that this cheat doesn't get the opportunity to cheat.

maths 
Well...,
As per the previous comment I won't giv you the fully worked solution itself. But if you can give an example of a possibility of these 3 groups I will sure give a hint.

maths 
Calvin,
Thanks for noticing, Shame. As such we have started tracking keshav's and mathlover's account( i.e. we are searching which accounts got these problems, and we are searching which accounts entered exactly the answers posted here, even if they are wrong at moreorless the same time or date). Currently we have pinpointed about five possibilities for keshav's account. A few more posts and he will be ours. Thanks for your cooperation, Shame.
Calvin Lin
Brilliant Maths Challenge Master