1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Viefleur [7K]
3 years ago
6

This problem is taken from the delightful book "Problems for Mathematicians, Young and Old" by Paul R. Halmos. Suppose that 681

tennis players want to play an elimination tournament. That means: they pair up, at random, for each round; if the number of players before the round begins is odd, one of them, chosen at random, sits out that round. The winners of each round, and the odd one who sat it out (if there was an odd one), play in the next round, till, finally, there is only one winner, the champion. What is the total number of matches to be played together, in all the rounds of the tournament
Mathematics
1 answer:
aleksley [76]3 years ago
4 0

Answer:

680 games

Step-by-step explanation:

Suppose that 681 tennis players want to play an elimination tournament.

1st round:

One of 681 players, chosen at random, sits out that round and 680 players play. There will be 340 winners plus one player which sits - 341 players for the next round and 340 games

2nd round:

There will be 170 winners plus one player which sits - 171 players for the next round and 170 games

3rd round:

There will be 85 winners plus one player which sits - 86 players for the next round and 85 games

4th round:

There will be 43 winners - 43 players for the next round and 43 games

5th round:

There will be 21 winners plus one player which sits - 22 players for the next round and 21 games

6th round:

There will be 11 winners  - 11 players for the next round and 11 games

7th round:

There will be 5 winners plus one player which sits - 6 players for the next round and 5 games

8th round:

There will be 3 winners  - 3 players for the next round and 3 games

9th round:

There will be 1 winner plus one player which sits - 2 players for the next round and 1 game

10th round - final:

1 champion and 1 game.

In total,

340 + 170 + 85 + 43 + 21 + 11 + 5 + 3 + 1 + 1 = 680 games

You might be interested in
1-908876655 percent
Dmitry [639]

Answer:

What is the question exactly?

Step-by-step explanation:

4 0
3 years ago
Which line has no slope?
zloy xaker [14]
A b is no slope and kL is undefined
5 0
3 years ago
A milk container capacity is one gallon. How many cups would that equal ?
nekit [7.7K]
<span>1 gallon = 4 quarts = 8 pints = 16 cups </span>
6 0
3 years ago
The difference of two numbers is equal to 0.6. Their quotient is also 0.6. What are the numbers? There are 4
Makovka662 [10]
Let the two numbers be represented by x and y. The problem statement gives rise to two sets of equations.
  x - y = 0.6
  y/x = 0.6 . . . . . . . assuming x is the larger of the two numbers
or
  x/y = 0.6 . . . . . . . assuming y has the larger magnitude

The solution of the first pair of equations is
  (x, y) = (1.5, 0.9)

The solution of the first and last equations is
  (x, y) = (-0.9, -1.5)

The pairs of numbers could be {0.9, 1.5} or {-1.5, -0.9}.
8 0
3 years ago
Which expression is the same as 10÷4?<br><br> 110 of 4<br><br> 4÷10<br><br> 110×14<br><br> 14 of 10
erica [24]

Answer:

1/4 of 10

Step-by-step explanation:

7 0
2 years ago
Other questions:
  • The solution set for 7q2 − 28 = 0 is <br> (Separate the solutions with a comma)
    11·2 answers
  • Suppose the spread of a direct contact disease in a school is modeled by the exponential function P(t) =
    14·1 answer
  • Is 4,400 10 times as much as 440
    7·2 answers
  • a. Create a real world problem using probability and post your word problem in the discussion area. If you are having trouble br
    10·1 answer
  • (x+4)^2=9<br> x=?<br> help please!
    10·2 answers
  • 1) Functions A, B and C are all linear functions ofx. Rank the rates of change and the y-intercepts of all three from smallest t
    5·1 answer
  • 5. Pencil crayons are stored in boxes of 10. There are 4 boxes of red, 3 boxes of blue, 5
    5·1 answer
  • A pizza has a diameter of 14 inches
    10·1 answer
  • 28 + 24 as a product of two factors using the GCF and the distributtive property
    14·1 answer
  • Can you help me I need to send this to my teacher like TODAY
    11·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!