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Amazon.com Manager Interview Question

I interviewed in Seattle, WA and was asked:
"If you had 5,623 participants in a tournament, how many games would need to be played to determine the winner"
Tags: brain teaser, algorithm, phone, math, intern, bs
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Answer

Part of a Manager Interview Review - one of 4,763 Amazon.com Interview Reviews

Answers & Comments

3
of 5
votes

Before I could figure that out, I'd need to know whether the # of participants represents the number of individuals on larger teams, or the number of teams

- anonymous on Apr 02, 2010
4
of 6
votes

A specific numerical answer can be given, but there are multiple ways the tournament can be setup, for example, are there play-in games, byes, etc. I would think the question is being given to a manager to see how they think and process, and then come up with a specific numerical answer, as opposed to just a math problem.

- Anonymous on Apr 02, 2010
8
of 8
votes

It can be just one game. A huge mock battle.

- Anonymous on Apr 02, 2010
19
of 23
votes

5,622. Assuming it is a single elimination tournament. All teams lose one game except the champs. It's always # of teams - 1

- Anonymous on Apr 03, 2010
0
of 3
votes

if each team plays until it loses in one(team)-on-one(team) contests, the answer is ln(5623)/ln(2)

- if each team plays until it loses on Apr 03, 2010
6
of 8
votes

Assuming it is a simple process of elimination, it takes 5622 losers to get 1 winner from 5623 participants. So, it would require 5622 games.

- key2success on Apr 04, 2010
1
of 3
votes

Assuming it is a simple process of elimination, it takes 5622 losers to get 1 winner from 5623 participants. So, it would require 5622 games.

- key2success on Apr 04, 2010
1
of 3
votes

if it's a 1:1 type draw, then # rounds = (5623)x where x is base 2. a good answer is between 12 and 13 rounds.

212 = 4096 so I'd draw up 13 rounds and give out 1,527 byes.

- tv on Apr 07, 2010
6
of 9
votes

There is no true answer as the question is very open ended.
The interviewer is probably looking at task delegation, management and creativity skills.

- NancyS on Apr 07, 2010
1
of 3
votes

One

- 0utOfTheBoX on Apr 07, 2010
2
of 5
votes

One. Obviously.

- Anonymous on Apr 08, 2010
3
of 4
votes

One game, all players participate.

- angle 72 on Apr 08, 2010
1
of 2
votes

If participants equal number of teams involved, think power of 2.

- WichitaKS10 on Apr 08, 2010
6
of 7
votes

The interviewer is not looking for the right answer because there can be many. What he/she is looking for is your logical approach in solving the answer. So you could start by probing more is first I would like to understand if 5,623 participants represent the number of team or individuals. Then ask the next logical question based on the answer.

- Mike on Apr 09, 2010
0
of 1
vote

Everyone who didn't ask a follow up question except Mike is right.

The question says, "if YOU had ...". This requires no follow up questions, because YOU should decide how YOU are going to operate YOUR tournament. Why would Mike or any of the others think it's someone else's job to organize his/her tournament.

- Nathaniel on Apr 11, 2010
1
of 3
votes

Oh just a follow up. My tournament would be held in the top of a hardly dormant volcano. Everyone would get a backpack full of grenades and the first one out of the crater without dying wins. That makes 1 game.

Also, I think most participants who got out of the volcano alive would consider themselves winners, but only one would get to keep the gold plated dancing chiquita banana.

Yipee!!!! I'm right too! Take that Mike!

- Nathaniel on Apr 11, 2010
3
of 3
votes

it'd be one game if it was a battle to the DEATH

- One, obviously on Apr 11, 2010
0
of 1
vote

I agree with Nancy there is no strict answer to this question it is all about problem solving. First thing to do is to get more information, if it is not forthcoming then make assumptions, as an interviewer I would not be impressed if the candidate didn't ask for more information, although I probably would not supply any more.

Then looking for a logical (and humane) answer which is substantiated with appropriate reasoning. Ie number of people on a team, game being played, what is required to win a match, are there several games in a match? knockout style tornamant sounds like a good approach.

- Angus on Apr 15, 2010
0
of 0
votes

I agree with Mike. Just show the interviewer how you think and how you will tackle the problem in a colloborative environment

- Vadim on Apr 15, 2010
1
of 1
vote

1

- maureen on Apr 15, 2010
0
of 0
votes

I agree with the very first response. Many of you are perhaps making the assumption that this is a one-on-one tournament such as singles tennis. Isn't it possible the question could refer to a soccer or basketball tournament where there are multiple players on each team? That would certainly bring the number of games to be played down considerably.

- just me on Apr 15, 2010
2
of 2
votes

I'd give an approximate answer, stating my assumptions. The question asked is not the number of rounds (2 people per game: log base 2, giving approximately 13 rounds with everyone playing at least one game ) - it's the number of games. So, if two people per game, then it's the sum of 5623/2 + 5623/4 + 5623/8 + 5623/16 + ... The limit of this is not something I know off the top of my head, but it's less than 5623. Also, interestingly, you need to account for the original number being odd. That could be accommodated in a number of ways, none of them straightforward.

- Dana on Apr 18, 2010
0
of 0
votes

5622 ... if based on elimination between 2.

- simplebrain on Apr 19, 2010
1
of 1
vote

I personally agree with most of you. If you read the posts here, you see all types of answers. Some say "1". Short and simple rules to a simple game. Others have posted all types of formulas and methods to figure out a process. The answers here are all a good example of different minds using different means to find an end. Those different answers are what a good interviewer would be looking for. If the job needs a person that is logical and takes time to plan things out, or perhaps someone that needs to think fast on their feet. That kind of question could come in handy for any kind of interview in my opinion.

- Craig on Apr 20, 2010
0
of 0
votes

1

- Zam on Apr 21, 2010
4
of 6
votes

I think the interviewer is asking you to ask for more information, ask three qualifieng questions to be exact in order to show you have the probing skills to fully understand a customers situation or company problem and have the ability to ask the appropriate questions to or to get the help to solve. Question 1) How many players are allowed per round? Question 2) Is there a time restriction on these rounds? (Daylight or Night as well) Question 3) Are there going to be different classes for the golfers? Are we taking handicaps into consideration? I guess there could be more questions but chances are the interviewer would stop you after the third question.

- chapped on Apr 21, 2010
9
of 10
votes

The correct answer is:

"I didn't come here to play bullst games for 8 hours, you Mac-slinging hipster. Ask me a real question."

- tired on Apr 22, 2010
1
of 1
vote

5622....................................assuming single elimination

- madhur on Apr 26, 2010
3
of 3
votes

5623 is a prime number. Good luck dividing into even teams. Also, there
is no use of the word "minimum" in the original question. This question is
a good example of a problem with no absolute answer. If I were to ask this
of an interview candidate (which I wouldn't because I think subjective
questions are mostly a waste of time for everyone involved), I would look
for someone who can:
A) Ask questions to pin down a few details.
B) Formulate options.
C) Suggest options with recommendation and take feedback.
D) Execute (pretty hard to demonstrate in the 10 minutes max I'd give this).

p.s. I'd hire chapped. Good answer!

- Toasty on Apr 26, 2010
0
of 0
votes

Depends on the numbers of players per team.

- Kevin on Apr 27, 2010
1
of 1
vote

'Excuse me, I'm just waiting for excel to open and my math wiz buddy in accounts to pick up to verify my calculation. I'll get back to you in two minutes with the answer.'

- ash on Apr 28, 2010
0
of 0
votes

'Excuse me, I'm just waiting for excel to open and my math wiz buddy in accounts to pick up to verify my calculation. I'll get back to you in two minutes with the answer.'

- ash on Apr 28, 2010
1
of 1
vote

I would try and be creative and put my suggestions in front of them while I give them a reason for all the options that I choose. For instance, I'd say I would create 5 levels for each game as adding more levels makes the game more challenging and interesting. I wouldn't want to set up too many games as it would require a lot of overhead using up a lot of resources for organizing large number of games. Hence, in each round I would eliminate 20 participants. That would make 100 players getting eliminated after every game. After every 10 games, I would allow all the eliminated contestants to battle it out and 15 can re-enter the game as the eliminated ones would get a chance to observe, learn, refresh and get a second chance... (The interviewer might stop me eventually before it gets too long).

Even though my answer was too long, I think I would show them how my logical thinking works. They would see that I am thinking aloud and in the end all that matters is how we approach the problem rather than giving them a vague answer with no reasoning.

- rational thinker on Apr 28, 2010
0
of 0
votes

Oh and I agree with Toasty, I would hire chapped :) I like the way they think.

- rational thinker on Apr 28, 2010
0
of 0
votes

Oh and I agree with Toasty, I would hire chapped :) I like the way they think.

- rational thinker on Apr 28, 2010
0
of 0
votes

i dont know how everybody else thinks butI divided by two with an extra game for when the number is odd and came up with 5627. the question was straight forward, " How many games"....

- kgar79 on May 01, 2010
0
of 0
votes

I would have been startled as well, just reading it. Congrats on keeping your calm!
My intuitive answer would have probably been:

Game theory - 1 or rather none - when it's a battle to death everyone loses, even the winner (last man standing, howling at the moon).

I would have likened it to the company and customer situation - in good company EVERYONE is a winner (win-win scenario).

Good luck with your endeavors!

- Tessa on Oct 03, 2010
0
of 0
votes

1. I think, this question is for a management position. The size of team is given as a too big random number. One cannot control a team of 5627. Divide them in a measure size, e.g size of 10 or 20 (any measureble size). With 10, there will ve 563, which can be further divided into 10, leading to apx 57. that can be futher divided into 10, leaving it to 6 teams. proformance/ goals can be set and can be evaluated later.

2. or do a marathon.

- pSandhu on Dec 31, 2010
0
of 1
vote

None. Our PC world demands everyone gets a trophy.

- Ed C on Dec 31, 2010
0
of 0
votes

*
Keep in mind the position, Nathaniel is right. YOU are organizing the tournament, make a rational decision and describe it. Your answer should be formulated to convey a skill.

For example I might suggest something like this:
1 on 1 round robin, 5,623 players, SUM(1+2+3+...+5621+5622) games

Quick and simple, shows some knowledge of algorithms but not very practical.
The 1st participant plays 5622 others, the 2nd plays 5621, until the 5622nd plays 1 (5623rd participant). Notice you don't add 5623. Participant with the most wins is the champion.

- Anonymous on Jan 03, 2011
1
of 1
vote

Supposed it is a single elimination.
should be 5626 games
because the first row would be 5623/2 = 2811.5
which means 1 person must be going to the next round to compete
therefore we will have 2812 contestants
then the second row would be 2812/2 = 1406
the third row would be 1406/2 = 703(odd number which means the one of them is going to the next round without a fight. ect...

- Anonymous on Jan 08, 2011
0
of 0
votes

I believe I would have responded with "Is that how many applicants there are for this job?" Followed by "One game, one victor."

- someone else on Jan 11, 2011
3
of 3
votes

Before answering you should read the interview report this question is linked from, where the question is explained in more detail -- """If you had 5,623 participants in a tournament, and each participant had to play games until he/she one or lost, and every game had a winner and loser, how many games would have to be played in order to determine the winner of the tournament"""

So it's pretty unambiguous: Participants are individuals; the tournament is single elimination; games involve just two parties (a winner and a loser.)

The question doesn't ask about the number of rounds involved, nor about timeframe. Just the sheer number of games.

So we're left with an answer of 5622 games (because every game has one and only one loser and 5623 - 1 participants need to lose for there to be a single participant left as the winner, so that's how many games there must be.)

- Jordan on Jan 11, 2011
0
of 0
votes

Assuming in each game "n" people participate and there is just one winner in a game. If N is the total number of people (in this case 5623), then the approximate number of games would be:
log(N)/log(g) -1

- Debarshi on Jan 11, 2011
1
of 2
votes

After each round, you would have half the number that started the previous round; except if it were an odd number it would he half + 1. So 13 rounds.

2812 1
1406 2
703 3
352 4
176 5
88 6
44 7
22 8
11 9
6 10
3 11
2 12
1 13

- Bob InNorCal on Jan 11, 2011
1
of 1
vote

It is far simpler than you guys are making it out to be. In ALL single elimination tournaments there is one less game than the number of participants. Because in every game 1 team gets eliminated. And at the end 1 team has to be left standing.

- PaulO on Jan 12, 2011
2
of 2
votes

This will be a detailed explanation.
Since they're asking for a tournament, that means one on one matches, and eliminations of 'participants' or players. With such a large number doing a round robin style tournament would not be very efficient, as every player would have to play every other player, ((N-1)^2)/2 =15,803,442 matches. I would first start to get more details of the tournament. If it were up to me to design the tournament and easily determine the number of matches, I would go with single elimination bracket because since its based on power of 2.

Contrary to what what Bob InNorCal did, you dont start halving the at the beginning with 5623, because its not power of 2. You will get to a point where there wont be even numbers, and BYEs will have to be given, it would be unfair to give byes out at the end or middle of the tournament, players would complain that others got BYEs and they didnt.

Detailed Explaination:
In a single elimination bracket, the brackets end with 1 match between 2 players, then 2 matches and 4 player, and eventually for this tournament, 4096 matches between 8192 players. But since we dont have 8192 players, there will have to be BYEs which wont count as matches. In this case we'll have to use a 8192 single bracket, with the first 4096 players spread every other position then the last 1527 players spread evenly throughout the bracket and the remaining 2569 positions are BYEs (4096 + 1527 + 2569 = 8192). Here are how the rounds look like:
A - 1527 matches, (4096 matches was suppose to happen, but 2569 BYEs are no counted)
B - 2048 matches,
C - 1024 matches,
D - 512 matches,
E - 256 matches,
F - 128 matches,
G - 64 matches,
H - 32 matches,
I - 16 matches,
J - 8 matches,
K - 4 matches
L - 2 matches,
M - 1 match

From round B-M, its (2^12)-1 = 4095, so with Round A, its 4095+1527=5622.
The calculated answer 5622 is one match less than the number of participants.

However, just because its easy with single elimination to determine the number of matches, does not mean that it is what they initially asked, conversing with the interviewer for more details of the tournament is important. If the interviewer said it was a double elimination tournament then a player would have to lose twice in the bracket to be eliminated from the tournament. Depending on the number of players and the placement of the BYEs, then calculating the number of matches in a true double elimination maybe difficult. Also in Double Elimination, the winner maybe won by someone without a loss or with 1 loss, the winner without a loss means one less game.

- CuriousG on Feb 13, 2011
0
of 0
votes

it is assumed that the competition is a head to head knockout competition like wimbledon. the only correct answer is 5,622. the quickest and smartest way to get that answer is to see that in a knockout tournament every body loses once and only once, except the winner. in every match, one person loses. therefore the number of matches required equals the number of players minus 1.

PaulO, Jordan, madhur, simplebrain and key2success you are all hired!

- marty holah on Jun 27, 2011
0
of 0
votes

How many games are played? Well all of them of course, how else do you find the winner.

- Clay Lovett on Jan 10, 2012
0
of 1
vote

It need only one game to find the winner

- irshad on Jun 10, 2012

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