bonanova Posted October 30, 2007 Report Share Posted October 30, 2007 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. Quote Link to comment Share on other sites More sharing options...
0 Guest Posted November 5, 2007 Report Share Posted November 5, 2007 Let's see if I get this, 97 contestants. Single elimination. wouldn't that be 97 matches? Quote Link to comment Share on other sites More sharing options...
0 bonanova Posted November 5, 2007 Author Report Share Posted November 5, 2007 Let's see if I get this, 97 contestants. Single elimination. wouldn't that be 97 matches? What if there were two contestants? Quote Link to comment Share on other sites More sharing options...
0 Guest Posted November 5, 2007 Report Share Posted November 5, 2007 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 Quote Link to comment Share on other sites More sharing options...
0 Guest Posted November 5, 2007 Report Share Posted November 5, 2007 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 Quote Link to comment Share on other sites More sharing options...
0 bonanova Posted November 5, 2007 Author Report Share Posted November 5, 2007 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. Quote Link to comment Share on other sites More sharing options...
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bonanova
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?
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