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There are 400 points on a plane. Prove that different distances among them are not less then 15.
In every cell of a board with sizes 5x5 cells sits a bug. At some moment all bugs crawl into neighbouring (on horizontal or vertical) cells. Will an empty cell remain?
A chessboard is given. It is allowed simultaneously to paint into another colour all cells located in a square 2x2. Is it possible to get only one black cell on the board?
A chessboard is given. It is allowed simultaneously to paint into another colour cells of any vertical or horizontal lines. Is it possible to get a board where there is only one black cell?
There are three pucks on a plane A, B and C. Hockey player hits one of the pucks in such a way that it went between two other pucks and stopped at some point. Is it possible for pucks to return on its initial place after 25 hits?
Еhere are n unparallel lines in pairs on a plane. Prove that the angle between two of them is not more then (180°/n).
Suppose candidate A receives 54% of the entire vote, but only 48% of the female vote. A voter is selected at random for an interview. What is the probability that the voter is a woman who voted for candidate A?
I do not understand waves fully. Can you explain?
Can i know that how can i lock my c++ program coding using password?
I need to do an assignment "Currency converter" with a numeric pad which converts euro dollar, pound and Mauritian rupees.








