I read the riddle from Jeff and it reminded me of my early work with thought process and how to apply it to puzzles, riddles etc.
Here is a good one.
There is a knockout tennis tournament e.g. Wimbledon and there are 312 entrants. How many games must be played to ensure a champion is crowned?
Another riddle
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JollyGreen
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It doesn't matter who wins it's a matter of how many games must be played?
What I'm getting at this this. Let's say you get everyone to play everyone in a particular round. Could you say 'the people who come in the bottom x places exit the competition, and if there are more than x people occupying those places than we throw a dice to decide who leaves'?
Jeff
Jeff
JollyGreen wrote:It doesn't matter who wins it's a matter of how many games must be played?
311 - is the number of losers you need to find a winner
and the long answer:
312/2=156 games 156 players
156/2=78 games 78 players
78/2=39 games 39 players
39/2=19 games 20 players
20/2=10 games 10 players
10/2=5 games 5 players
5/2=2 games 3 players
3/2=1 game 2 players
2/2=1 game 1 player
and the long answer:
312/2=156 games 156 players
156/2=78 games 78 players
78/2=39 games 39 players
39/2=19 games 20 players
20/2=10 games 10 players
10/2=5 games 5 players
5/2=2 games 3 players
3/2=1 game 2 players
2/2=1 game 1 player
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JollyGreen
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I've posted this before and the reason I posted it again was to highlight how people think about things. The answer is always n-1 where n is the number of entrants. I am not sure but I think I discussed this with PeterLe as some point or fair play to him he is thinking along the right lines.
Our thought processes are flawed and most people think about things the wrong way. With many things it is a case of working the opposite way round so in this case only 1 player can win therefore the remainder are losers and therein lies your answer n-1.
I am not sure if it was only on here but on one forum a few years back one person argued and argued that it was not correct and my thought process and logic were flawed. He set about proving it with some algebra and surprise surprise he came to the same answer as me every time. Difference being it took me less than a second to arrive at the answer and he took ages writing his formulas.
Jeff, there is a message here that you over analyse things. I am not being disrespectful, you have known me long enough to realise that is not my style. It's just that you are looking for problems when they don't exist.
I always say KISS...keep it simple stupid. It is also a case of Lex Parsimoniae
Our thought processes are flawed and most people think about things the wrong way. With many things it is a case of working the opposite way round so in this case only 1 player can win therefore the remainder are losers and therein lies your answer n-1.
I am not sure if it was only on here but on one forum a few years back one person argued and argued that it was not correct and my thought process and logic were flawed. He set about proving it with some algebra and surprise surprise he came to the same answer as me every time. Difference being it took me less than a second to arrive at the answer and he took ages writing his formulas.
Jeff, there is a message here that you over analyse things. I am not being disrespectful, you have known me long enough to realise that is not my style. It's just that you are looking for problems when they don't exist.
I always say KISS...keep it simple stupid. It is also a case of Lex Parsimoniae
Last edited by JollyGreen on Sun Mar 24, 2013 10:10 am, edited 1 time in total.
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JollyGreen
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They're called byes Jeff. You are over thinking it.Ferru123 wrote:What I'm getting at this this. Let's say you get everyone to play everyone in a particular round. Could you say 'the people who come in the bottom x places exit the competition, and if there are more than x people occupying those places than we throw a dice to decide who leaves'?
Jeff
Maybe I sometimes do, but the devil is often in the detail and this is a case in point.JollyGreen wrote: Jeff, there is a message here that you over analyse things. I am not being disrespectful, you have known me long enough to realise that is not my style. It's just that you are looking for problems when they don't exist.
With the solution proposed, you're potentially going to have to rely on a dice tossing method to decide who qualifies. If that's part of the rules of the game, then fine, but it was worth checking the parameters.
Jeff
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JollyGreen
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Jeff
This process occurs in every knock-out tournament, if there are an odd number of entrants then someone gets a bye to the next round. There is no devil in the detail and you do not need to check and double check the dice tossing. I didn't ask who the best player was and I didn't mention seeding etc. I merely asked if 312 players enter a knock-out tournament how many matches are required to crown the champion?
The answer will always be n-1
JG
This process occurs in every knock-out tournament, if there are an odd number of entrants then someone gets a bye to the next round. There is no devil in the detail and you do not need to check and double check the dice tossing. I didn't ask who the best player was and I didn't mention seeding etc. I merely asked if 312 players enter a knock-out tournament how many matches are required to crown the champion?
The answer will always be n-1
JG
By offering someone a bye to the next round, you are introducing a new parameter into the equation. The original question said nothing about a bye. I assumed that everyone plays the same number of games per round, i.e. no player was awarded an advantage due to randomness.JollyGreen wrote:Jeff
This process occurs in every knock-out tournament, if there are an odd number of entrants then someone gets a bye to the next round.
As I was unsure of the rules, I questioned what the rules are. Questioning definitions is a fundamental part of critical thinking, and in no way constitutes over-analysis.
As an aside, I did consider giving players a bye, but I thought 'No, that would be over-complicating things. After all, there's nothing in the rules about byes, so I'd be solving a different puzzle'.
Jeff
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JollyGreen
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Jeff
Penultimate post. You just don't get it my friend. Irrespective of byes, coin tosses etc etc the answer is always n-1
You will notice other forumites gave the correct answer and they were spot on in their thinking.
I'm in the middle of something but when I have some time I will give you the math and then you hopefully will get it
JG
Penultimate post. You just don't get it my friend. Irrespective of byes, coin tosses etc etc the answer is always n-1
You will notice other forumites gave the correct answer and they were spot on in their thinking.
I'm in the middle of something but when I have some time I will give you the math and then you hopefully will get it
JG