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Tennis tournament


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#1 bonanova

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Posted 30 October 2007 - 09:19 AM

You are the director for the annual Open city-wide Men's Singles Tournament.
So you're in charge of drawing up the brackets and seeding the entries.
Your job will be easiest if the entrants number a power of two.

As luck would have it, 97 locals sign up. But at least they all have distinct
rankings, so the seeding is straightforward; and, since it's a single-elimination
format, there is no losers bracket. But since there's an odd number of entrants,
you'll need some play-in matches to start, and maybe some byes for the
higher seeds
. Eventually you can reduce the number of surviving players
to a power of two, and the rest of the pairings are straightforward.

You spend a sleepless night working on it and finally come up with a
set of brackets that work.

How many matches are in the brackets that you drew up?

Spoiler for solution

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The greatest challenge to any thinker is stating the problem in a way that will allow a solution.
- Bertrand Russell

#2 hipowertech

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Posted 05 November 2007 - 04:43 PM

Let's see if I get this,
97 contestants.
Single elimination.
wouldn't that be 97 matches?
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#3 bonanova

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Posted 05 November 2007 - 05:04 PM

Let's see if I get this,
97 contestants.
Single elimination.
wouldn't that be 97 matches?

What if there were two contestants?
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The greatest challenge to any thinker is stating the problem in a way that will allow a solution.
- Bertrand Russell

#4 belegoth

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Posted 05 November 2007 - 07:53 PM

Single elimination means 1 man eliminated in every match. Since the winner is supposed to stay unbeaten, that means:
= - 1;
or N = 97--; therefore N==96.
Hope it's clear now
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#5 hipowertech

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Posted 05 November 2007 - 09:20 PM

okay, fair enough. I broke the cardinal rule of problem solving.....
I rushed my answer.
there go my chances for a shot at mensa. lol

nice one though bonanova.

Peace
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#6 bonanova

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Posted 05 November 2007 - 11:35 PM

okay, fair enough. I broke the cardinal rule of problem solving.....
I rushed my answer.
there go my chances for a shot at mensa. lol

nice one though bonanova.

Peace

You can join my organization ...
DENSA - Diversely educated - not seriously affected.
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The greatest challenge to any thinker is stating the problem in a way that will allow a solution.
- Bertrand Russell




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