Due: Prof. Titu Andreescu’s 104 Combinatorial Problems from Training of USA IMO Team.
Call a 7-digit telephone number memorable if the prefix sequence is exactly the same as either of the sequences or (possibly both). Assuming that each can be any of the ten decimal digits , find the number of different memorable telephone numbers. (AHSME 1998)
Two of the squares of a checkerboard are painted yellow and the rest are painted green. Two colour schemes are called equivalent if one can be obtained from the other by a rotation in the plane of the board. How many inequivalent colour schemes are possible? (AIME 1996)
Kindly share your solutions, comments,