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
Which type of correlation would you expect to see between the distance traveled and the time it takes to travel that distance? A
k0ka [10]
Positive because they would both be increasing
5 0
2 years ago
Read 2 more answers
Why is it helpful to write numbers in different ways
Goshia [24]
You should write numbers in as many ways as you possibly can to make new connections in your brain. Knowing how to write numbers in many different ways can help you solve complex problems more easily. Doing this can also reinforce the mathematical principles and logic you have memorised.

Writing one in many different ways:

1=1/1=2/2=3/3=4/4=(-1)/(-1)=(-2)/(-2)

=1.0=1.00=1.000=(1/2)+(1/2)=(1/3)+(1/3)+(1/3)

=(1/4)+(1/4)+(1/4)+(1/4)

Writing a half in many different ways:

1/2=(1/4)+(1/4)=(1/6)+(1/6)+(1/6)

=(1/8)+(1/8)+(1/8)+(1/8)=4*(1/8)

=2/4=3/6=4/8=5/10=0.5=0.50

etc...etc...
6 0
3 years ago
What is cos q if sec q = 2? I need help please please
nirvana33 [79]
I hope this helps you


sec Q=1/cos Q


2=1/cos Q


cos Q= 1/2


Q=30+2.pi.n


Q=330+2.pi.n


n€Z


6 0
3 years ago
The table below shows the scores of a group of students on a 10-point quiz.Test ScoreFrequency3 54 15 16 27 28 49 310 1The mean
Katarina [22]

Explanation

Part A

We can use the formula below to find the mean.

\text{Mean}=\sum ^{}_{}(\frac{fx}{f})

We will then have;

\begin{gathered} \text{Mean = }\frac{5\times3+4\times1+5\times1+6\times2+7\times2+8\times4+9\times3+10\times1}{19}=\frac{15+4+5+12+14+32+27+10}{19} \\ =\frac{119}{19}=6.2632 \end{gathered}

Mean = 6.2632

Part B

Since the data set is odd.

\begin{gathered} \text{Median}=\frac{(n+1)}{2}^{th}\text{observation} \\ =\text{Value of }\frac{\text{(19+1)}}{2}^{th}\text{observation} \\ =\text{value of 10th observation} \end{gathered}

Answer: From the column of cumulative frequency cf, the median is 7

5 0
1 year ago
Please help i will give brainliest
erma4kov [3.2K]

Answer:

it is 42 degrees

Step-by-step explanation:

the angle x is the same as the parallel angle

7 0
2 years ago
Read 2 more answers
Other questions:
  • How many times does the graph of 4x = 32 - x2 cross the x-axis ?
    12·2 answers
  • Express the complex number in trigonometric form. 3
    11·2 answers
  • How many gallons of a 30% salt solution must be added to 40 gallons of a 12% salt solution to obtain a 20% solution?
    12·1 answer
  • 6 divided by 603 is?
    14·2 answers
  • Solve the inequality. Enter the answer as an inequality that shows the value of the variable; for example f > 7, or 6 < w.
    6·1 answer
  • 12^{3}-9x^{2}-4x+3 in factored form by grouping
    11·1 answer
  • Define intersecting lines
    10·1 answer
  • Helppp !!!! .......................................................................
    13·1 answer
  • Please help me it's the lateral area of a cone along with the surface area
    7·1 answer
  • A farmer sells 8.2 kilograms of apples and pears at the farmer's market. 1/4 of this weight is
    12·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!