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# Tennis tournament

## Question

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?

96.

Play-ins, seedings, byes don't change this.

Each match eliminates an entrant and you need one survivor.

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Let's see if I get this,

97 contestants.

Single elimination.

wouldn't that be 97 matches?

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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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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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okay, fair enough. I broke the cardinal rule of problem solving.....

there go my chances for a shot at mensa. lol

nice one though bonanova.

Peace

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okay, fair enough. I broke the cardinal rule of problem solving.....

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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