Basketball throws: a rather intriguing puzzle
I had run into this problem long time back. I ran into it again last week. Thought will post it. See if you can solve it without using Google to find the answer. If not, then Google it – pretty interesting, huh? (I will post the answer later).
A basketball player keeps track of his throws for a full calendar year. He, of course, misses a few shots and succeeds with a few more. He missed the very first shot of the year. But he ended the year with 83% successful shots. You have to prove that there had to be a point where is success rate was exactly 75%.
Hint: this is not necessarily true for any number – e.g. 60%. But it is always true for 75%.
In fact, can you guess what are the other % (other than 75%) for which this is also true?