# How many cricket matches have to be played?

There are N teams in a cricket match. How many matches have to be played to know the winner and the runner-up?

Generalized solution for N teams.

__WIN Rs.100 PayTm cash__Answer this question and top voted answer’s author will be rewarded Paytm cash on registered email.

**[WINNER – Sambamurthy Bandaru(bsm)]**

Answer is “n-1”.

Assumption: question is to find the minimum matches to be played

How:

for each match played one team is eliminated. thus in first round, n/2 matches are played.

in second round n/4 are played

.

.

process is continued still one team is left.

so total=n/2+n/4+n/8+….+1

=1+2+4+…+n/2

this is in geometric progression with a=1, r=2, no. of terms =??(say k)

for each match played one team is eliminated. thus after first round, n/2 teams are left.

after 2nd round , n/4 teams are left

.

.

after ‘k’th round n/(2^k) teams are left

Now for n/(2^k)=1 team

=>n=2^k

=>k=log(n)

a=1,r=2,k=log n (base 2)

total matches = a(r^n – 1)/(r-1)

=2^(log n) -1

=n-1

Congratulations on winning puzzleFry Cricket Puzzle Contest.

You won Rs100 payTm Cash. Check your registered email.

[email protected]

n-1.

when each match is played a team gets eliminate so after 1st round n/2 teams remains

in next n/4

and so on

till one team remains.

therefore

=n/2+n/4+…………+1

=1+2+4+………….._n/4+n/2

this is a GP sequence

a=1 r=2

and no. of terms = x(assumed)

after each match, one team is eliminated. thus after first round, n/2 teams are left.

after 2nd round , n/4 teams are left

and so on

after k th round

n/(2^k) teams are left

Now for n/(2^k)=1 team

n=2^k

k=log(n)

a=1

r=2

k=log n (base 2)

total matches = a(r^n – 1)/(r-1)

=2^(log n) -1

=n-1

hence answer is n-1

n = number of teams,

x = a variable

When n is in order of 2^x,

for example, n = 2^4 = 16, then number of matches will be n-1 = 16-1 = 15 (simple GP)

But when n is not in order of 2^x,

for example, n = 21,

then number of matches will be n-1 = 21-1 = 20???

Lets check this, n = 21 = 16 + 5 = 16 + 4 + 1 (all in order of 2^x like, 2^4+2^2+2^0)

when n is in order of 2^x, then i can use n-1 for finding the matches.

for 16 teams = 15 matches

for 4 teams = 3 matches

for 1 team = 0 match

winner of these 2 groups needs to play again, along with the remaining 1 team. (total 3 teams remaining, say N)….

hence, N = 3 = 2+1 (again in order of 2^x)

for 3 teams = 2 matches are required for deciding the winner, who is none but the winner of all 21 teams.

Total matches to decide a winner =15+3+2 = 20 matches. that is (n-1).

Genarilized solution will be n-1.

Its just similar to 25 Horse and 5 track puzzle (First solve it)

Lets say N=10

Here we have,

12 Teams(Horses) and 2 (Teams can play a match)Track and find Top 2

MATCH #1 – **5 Matches **

A1 – B1

A2 – B2

A3 – B3

A4 – B4

A5 – B5

A6 – B6

Lets say, all A’s are winner

So,

MATCH #2 – Next tournament(**3 Matches**)-

A1-A2

A3-A4

A5-A6

Now we have winner- A1,A3 and A5

MATCH #3 – Next Tournament – (**3 Matches**)

A1-A3

A3-A5

A1-A5

Now we’ll get 2 winners lets say – A1,A3(A1 is winner and A3 runnerup)

In MATCH #4 – (**1 Matches**)

We’ll take winners opponent in MATCH #2 – A1’s opponent is** A4
**

**A4 –**A3

**Lets say**

**A4**win

In MATCH #5**-(1 Matches)
**We’ll take winners opponent in MATCH #1- A1’s Opponent

**B1**

B1 – A4

B1 – A4

Lets B1 wins So, B1 is 1st Runnerup.

Lets B1 wins So, B1 is 1st Runnerup.

A total of 14 Matches required to find out Winner and runner up in 12 Teams.

**It is not a generalized solution** but only a way

**n-1** is the correct answer

After each match is played a team will get eliminated so after 1st round n/2 teams remain

in next n/4 will remain in tournament and so on…………..till one team remains.

therefore

=n/2+n/4+…………+1

=1+2+4+…………..n/4+n/2

this is a Geometric Progression sequence with a=1 & r=2

after each match, one team will get eliminated. thus after first round, n/2 teams are left.

after 2nd round , n/4 teams are left

This implies after k th round

n/(2^k) teams are left

Now for n/(2^k)=1 team

n=2^k

k=log(n)

a=1

r=2

k=log n (base 2)

**Total matches** = a(r^n – 1)/(r-1)

=2^(log n) -1

**=n-1**

Complete Copy of

### Your Answer

## More puzzles to try-

### What is the logic behind these ?

3 + 3 = 3 5 + 4 = 4 1 + 0 = 3 2 + 3 = 4 ...Read More »### Defective stack of coins puzzle

There are 10 stacks of 10 coins each. Each coin weights 10 gms. However, one stack of coins is defective ...Read More »### Which clock works best?

Which clock works best? The one that loses a minute a day or the one that doesn’t work at all?Read More »### (Advanced) Cheryl’s Birthday Puzzle

Paul, Sam and Dean are assigned the task of figuring out two numbers. They get the following information: Both numbers ...Read More »### Five greedy pirates and gold coin distribution Puzzle

Five puzzleFry ship’s pirates have obtained 100 gold coins and have to divide up the loot. The pirates are all ...Read More »### Magical flowers!!

A devotee goes to three temples, temple1, temple2 and temple3 one after the other. In front of each temple, there ...Read More »### Tuesday, Thursday what are other two days staring with T?

Four days are there which start with the letter ‘T‘. I can remember only two of them as “Tuesday , Thursday”. ...Read More »### How could only 3 apples left

Two fathers took their sons to a fruit stall. Each man and son bought an apple, But when they returned ...Read More »### How Many Eggs ?

A farmer is taking her eggs to the market in a cart, but she hits a pothole, which knocks over ...Read More »### HARD MATHS – How much faster is one train from other Puzzle

Two trains starting at same time, one from Bangalore to Mysore and other in opposite direction arrive at their destination ...Read More »### Most Analytical GOOGLE INTERVIEW Question Revealed

Let it be simple and as direct as possible. Interviewer : Tell me how much time (in days) and money would ...Read More »### Lateral thinking sequence Puzzle

Solve this logic sequence puzzle by the correct digit- 8080 = 6 1357 = 0 2022 = 1 1999 = ...Read More »### How did he know?

A man leaves his house in the morning to go to office and kisses his wife. In the evening on ...Read More »### Pizza Cost Math Brain Teaser

Jasmine, Thibault, and Noah were having a night out and decided to order a pizza for $10. It turned out ...Read More »### Which letter replaces the question mark

Which letter replaces the question markRead More »### Which room is safest puzzle

A murderer is condemned to death. He has to choose between three rooms. The first is full of raging fires, ...Read More »### Richie’s Number System

Richie established a very strange number system. According to her claim for different combination of 0 and 2 you will ...Read More »### Srabon wanted to pass

The result of math class test came out. Fariha’s mark was an even number. Srabon got a prime!! Nabila got ...Read More »### Become Normal!!

Robi is a very serious student. On the first day of this year his seriousness for study was 1 hour. ...Read More »### Sakib Knows The Number!

Ragib: I got digits of a 2 digit number Sakib: Is it an odd? Ragib: Yes. Moreover, the sum of ...Read More »