AoPS Subset Problem

Algebra
Tutor: None Selected Time limit: 1 Day

Let S be a subset of {1, 2, 3, 4...., 100}, containing 50 elements. How many such sets have the property that every pair of numbers in S has a common divisor that is greater than 1?

Aug 18th, 2015

Thank you for the opportunity to help you with your question!

HELLO...Monkeys 

 have one doubt  in your question 

{1, 2, 3, 4...., 100}, containing 50 elements.

 how only 50 elements will be  from  1 to 100  please  recheck the question and tell to me 

 so that I can help you..

thank you!!!!

Please let me know if you need any clarification. I'm always happy to answer your questions.
Aug 18th, 2015

I already answered it thank you though!!!

Aug 18th, 2015

ok.. thanx.. do you have any other  question ??

 

Aug 18th, 2015

A four by four grid of unit squares contains squares of various sizes (1 by 1 through 4 by 4), each of which are formed entirely from squares in the grid. In each of the 16 unit squares, write the number of squares that contain it. For instance, the middle numbers in the top row are 6s because they are each contained in one 1x1 square, two 2x2, two 3x3, and the one 4x4

What is the sum of all numbers in a 10x10 grid?

Aug 18th, 2015

  the 

1 ^2 + 2^2+ 3^2 --------  up to 10^2

 by using  the formula of  the sum of square  of n natural no 

 S^2  =  n(n+1) (2n+1)/6

 where n  = 10

 10 *11*21/6 =     385

 regarding further clarification please let me know ...

I will be happy to help you 

Thank you !!!

Aug 18th, 2015

No...ignore the question, can you understand the first part of it?

Aug 18th, 2015

sry .. not 

Aug 18th, 2015

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