Once my friend asked me, do you know knockout series. I said yes. He said, "well then tell me how many matches will be played among 500 players"? If you are able to give this answer than tell me how much matches will be played among 1000 players? But in the later question if you have taken time more than 30 sec then you are gone.......
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Genral thinking will start like this:
ReplyDeleteSo, 500 players, so
First level of matches will be 250.
Second level of matches will be 125.
Third level of matches, ohh we have odd number. So question will come in mind, now what??
So lets ask to my friend,
"Hey there is flaw in question. We cann' have a knockout, until players will be 2 raise to n(2^n)."
Here is his reply,
In the odd number of player cases the top ranked player will be through to that level.
Now tell me?
So carry forwarding earlier solution,
ReplyDeleteFirst level of matches will be 250.
Second level of matches will be 125.
third level of matches will be 112.
66
33...
So on.
So now , series become,
N/2 + N/4 + N/8 ..... +1.
So , it is series. a GP (Remember GP J. If yes then what it is summation of GP term).
Great If you come with the solution of 499 in case of 500 player and 999 in case of 1000. So it is (N-1).
ReplyDeleteNow think of solution sincerly . Any thing strikes???
Dude, finally there is only one winner and all other player will be knocked out. Each knocked out matches throw out only one player. So, the total knocked matches will be N-1. Easy......
ReplyDeleteNow you feel like dumb ....
No. You have thought of this earlier then you are a genious. Sorry THE Genious.