Twenty points lie on a circle, so as to form a regular polygon. Then they are split into ten pairs, and the points in each pair are connected by a chord. Prove that some pair of these chords have the ...
Anyone have any ideas on this question? I think you have to use the pigeon hole principle..but I am not sure about that? The numbers $1,2,3,\ldots,101$ are written down in a row in some order. Is ...
Here's a riddle that I've been struggling with for a while: Let $A$ be a list of $n$ integers between 1 and $k$. Let $B$ be a list of $k$ integers between 1 and $n$. Prove that there's a non-empty ...
In a group of 200 people, number of people having at least primary education (assuming - Category I): number of people having at least middle school education (Category II): number of people having ...
One of my friends found this riddle. There are 100 soldiers. 85 lose a left leg, 80 lose a right leg, 75 lose a left arm, 70 lose a right arm. What is the minimum number of soldiers losing all ...