![Bassoonist](/avatars/31171.jpg)
Bassoonist
29.01.2020 •
Mathematics
Me. my math teacher said that there is some sort of pattern that will us understand how to win the game. here is what the question is:
you will be competing with other contestants for a grand prize of 1 million dollars. all of the contestants will form a circle around the host. starting at seat #1, the person to the left of that contestant seat #1 is out of the game. the next remaining contestant is in seat #3. the person left of that remaining contestant is out of the game. this pattern continues until there is one contestant remaining. the object is simple. determine what seat # you must sit on the circle in order to be the last contestant remaining. since you do not know how many contestants are on the show, you must come up with an explanation of how to win at this game.
you friends!
Solved
Show answers
More tips
- H Horoscopes, Magic, Divination Where Did Tarot Cards Come From?...
- S Style and Beauty How to Make Your Lips Fuller? Ideas and Tips for Beautiful Lips...
- S Style and Beauty How are artificial nails removed?...
- F Family and Home How to Sew Curtain Tapes: Best Tips from Professionals...
- H Horoscopes, Magic, Divination How to Cast a Love Spell on a Guy? Guide for Guys...
- F Family and Home How to Properly Use a Water Level?...
- L Legal consultation What Documents Are Required for a Russian Passport?...
- H Health and Medicine How to Treat Styes: Causes, Symptoms, and Home Remedies...
- F Family and Home Protect Your Home or Apartment from Pesky Ants...
- T Travel and tourism Lost in the Catacombs: What to Do?...
Answers on questions: Mathematics
- M Mathematics For reasonable distances, a certain jogger can maintain an average speed of 6 miles per hour while running on level ground. the jogger decides to go to a local park and use one of...
- M Mathematics (04.03) mike forgot to replace the cap on a bottle of room freshener. the room freshener began to evaporate at the rate of 15% per day. if the original amount of room freshener in...
- M Mathematics What is the slope of the line that passes through the points (–1, –17) and (–4, –2)?...
- M Mathematics Name the factors in each of the following problems. a. 6 × 12 = 72 b. 8 × 9 = 72 c. 4 × 4 = 16 d. 3 × 7 = 21...
- M Mathematics Iwill choose brainliest answer (once it shows up)a.) rectangleb.) pentagonc.) trapezoidd.) trianglea rectangular pyramid is sliced parallel to its base as shown in the figure.what...
- M Mathematics Choco-chippy cookie company has two different manufacturing plants. company officials want to test whether each plant fills the bags with the same number of ounces. a random sample...
- M Mathematics Running uphill the jogger runs c mph slower than 6 mph. write an expression representing a speed of c mph slower than 6 mph....
- M Mathematics Where are the x-intercepts for f(x) = 4 cos(2x − π) from x = 0 to x = 2π? a) x = pi over 4, x = 3 pi over 4, x = 5 pi over 4 b) x = pi over 2, x = 3 pi over 2 c) x = pi over 4, x =...
- M Mathematics The ages (in years) of the 6 employees at a particular computer store are 44, 46, 40, 34, 29, 41assuming that these ages constitute an entire population, find the standard deviation...
- M Mathematics Megan claims that her horse can do simple addition problems. she showed her horse eight different cards with simple addition problems, and the horse was able to tap his foot to indicate...
Ответ:
Let n = number of players
The chart showing the values of n and the final winners is shown below in the attached image.Drawing out each scenario is optional, but it helps visualize what is going on.
Let's play out scenarios for n = 2 through n = 12 to see what the pattern might be.
------------------
n = 2 players
Seat #1 eliminates seat #2
Winner = seat #1
This is fairly trivial and boring as there is only one round and one elimination.
------------------
n = 3 players
Seat #1 eliminates seat #2
Seat #3 eliminates seat #1
Winner = seat #3
Like with n = 2, this game is over in one round. For n = 4 and greater, we'll start to see multiple rounds.
------------------
n = 4 players
Start of Round 1
Seat #1 eliminates seat #2
Seat #3 eliminates seat #4
End of Round 1
Seats remaining = {seat #1, seat #3}
Start of Round 2
Seat #1 eliminates seat #3
End of Round 2
Winner = seat #1
------------------
n = 5 players
Start of Round 1.
Seat #1 eliminates seat #2
Seat #3 eliminates seat #4
Seat #5 eliminates seat #1
End of Round 1.
Seats remaining = {seat #3, seat #5}
Start of Round 2.
Seat #3 eliminates seat #5
End of Round 2
Winner = seat #3
------------------
n = 6
Start of round 1.
Seat #1 eliminates seat #2
Seat #3 eliminates seat #4
Seat #5 eliminates seat #6
End of Round 1
Seats remaining = {seat #1, seat #3, seat #5}
Start of round 2
Seat #1 eliminates seat #3
Seat #5 eliminates seat #1
End of Round 2
Winner = seat #5
------------------
Up next is n = 7 players
Start of round 1.
Seat #1 eliminates seat #2
Seat #3 eliminates seat #4
Seat #5 eliminates seat #6
Seat #7 eliminates seat #1
End of Round 1
Seats remaining = {seat #3, seat #5, seat #7}
Start of round 2
Seat #3 eliminates seat #5
Seat #7 eliminates seat #3
End of Round 2
Winner = seat #7
------------------
n = 8 players
Start of Round 1
Seat #1 eliminates seat #2
Seat #3 eliminates seat #4
Seat #5 eliminates seat #6
Seat #7 eliminates seat #8
End of Round 1
Seats remaining = {seat #1, seat #3, seat #5, seat #7}
Start of round 2
Seat #1 eliminates seat #3
Seat #5 eliminates seat #7
End of Round 2
Seats remaining = {seat #1, seat #5}
Start of Round 3
Seat #1 eliminates seat #5
End of Round 3
Winner = seat #1
------------------
n = 9 players
Start of Round 1
Seat #1 eliminates seat #2
Seat #3 eliminates seat #4
Seat #5 eliminates seat #6
Seat #7 eliminates seat #8
Seat #9 eliminates seat #1
End of Round 1
Seats remaining = {seat #3, seat #5, seat #7, seat #9}
Start of round 2
Seat #3 eliminates seat #5
Seat #7 eliminates seat #9
End of Round 2
Seats remaining = {seat #3, seat #7}
Start of Round 3
Seat #3 eliminates seat #7
End of Round 3
Winner = seat #3
------------------
n = 10 players
Start of Round 1
Seat #1 eliminates seat #2
Seat #3 eliminates seat #4
Seat #5 eliminates seat #6
Seat #7 eliminates seat #8
Seat #9 eliminates seat #10
End of Round 1
Seats remaining = {seat #1, seat #3, seat #5, seat #7, seat #9}
Start of Round 2
Seat #1 eliminates seat #3
Seat #5 eliminates seat #7
Seat #9 eliminates seat #1
End of Round 2
Seats remaining = {seat #5, seat #9}
Start of Round 3
seat #5 eliminates seat #9
End of Round 3
Winner = seat #5
------------------
n = 11 players
Start of Round 1
Seat #1 eliminates seat #2
Seat #3 eliminates seat #4
Seat #5 eliminates seat #6
Seat #7 eliminates seat #8
Seat #9 eliminates seat #10
Seat #11 eliminates seat #1
End of Round 1
Seats remaining = {seat #3, seat #5, seat #7, seat #9, seat #11}
Start of Round 2
Seat #3 eliminates seat #5
Seat #7 eliminates seat #9
Seat #11 eliminates seat #3
End of Round 2
Seats remaining = {seat #7, seat #11}
Start of Round 3
Seat #7 eliminates seat #11
End of Round 3
Winner = seat #7
------------------
n = 12 players
Start of Round 1
Seat #1 eliminates seat #2
Seat #3 eliminates seat #4
Seat #5 eliminates seat #6
Seat #7 eliminates seat #8
Seat #9 eliminates seat #10
Seat #11 eliminates seat #12
End of Round 1
Seats remaining = {seat #1, seat #3, seat #5, seat #7, seat #9, seat #11}
Start of Round 2
Seat #1 eliminates seat #3
Seat #5 eliminates seat #7
Seat #9 eliminates seat #11
End of Round 2
Seats remaining = {seat #1, seat #5, seat #9}
Start of Round 3
Seat #1 eliminates seat #5
Seat #9 eliminates seat #1
End of Round 3
Winner = seat #9
------------------
Admittedly this is a lot of things to keep track of and it's easy to get lost. Hopefully the process is fairly straight forward even if it requires a lot of drawings.
The chart showing the values of n and the final winners is shown below in the attached image.Each pattern block is color coded to separate the start and stop of each sequence. Note the pattern of {1,3} then {1,3,5} then {1,3,5,7} then {1,3,5,7,9} and so on. The next pattern block would likely be {1,3,5,7,9,11}. This table will help you determine what seat you will want to sit in if you know how many players there are at the start. Of course you won't know ahead of time how many players there are, but when it comes to you picking your seat you can quickly look at the table (either on the paper or just something you memorize) and you can select the ideal seat based on what n is.
Ответ: