**Due: **Prof. Titu Andreescu’s 104 Combinatorial Problems from Training of USA IMO Team.

**Problem 1:**

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)

**Problem 2:**

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,*

Nalin Pithwa

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636

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please explain as much as possible, though

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question_2 we give yellow color any two blocks of the board there are 49*48 ways of doing it and the rest be green then observe that due to the square figure of the board there are 4 Rotationally symmetric case of every single 49*48 cases therefore (49*48)/4 therefore 588 cases

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