Combinatorics | Number Theory Answers

Let S be a square region (in the plane) of side length 2 inches. Show that among any nine points in S, there are three which are the vertices of a triangle of area ≤ ½ square inch

Let A be any set of 20 distinct integers chosen from the arithmetic progression 1,4,7, - . . , 100.
Prove that there must be two distinct integers in A whose sum is 104

If o(E) = 5:7, find o(E').
o(E') =

Ten women are fishing all in a row in a boat. One seat in the center of the boat is empty. The five women in the front of the boat want to change seats with the five women in the back of the boat. A person can move from her seat to the next empty seat or she can step over one person without capsizing the boat. What is the minimum number of moves needed for the five women in front to change places with the five women in back?
_1 _2 _3 _4 _5 __ _6 _7 _8 _9 _10

the sum of all decimal number 0.xyz (where x, y, and z are distinct digits) are...

there are 600 people residing in a campus. out of these 340 people take Hindustan Times news paper and 270 people take the Times of India. There are 70 people who take both the papers. Find the number of persons who do not take either of the two papers..//

prove the relation a=L(mod m) is aequivalent relation?

How many ordered 5-subsets of {0,...,9} are there? How many of these start with 0? How many positive integers of exactly 5 digits, but with no two digits the same are there? (In base 10)