A Crazy Math Question????

Question

There are 75 students in a PE class. Every student in the
class plays exactly one 1-0n-1 basketball game with every other student
in the class. How many total games will be played?

My guess is 75 times 75= 5,625 Is this right? If not where did I go wrong?

Thanks,

Alex

Answer 1

This is a simple problem.
Just get some of your friends together and act it out on a smaller scale.
Say you get 4 of your friends, you play each of them.
That's 4 games so far.
The next person then plays 3 games, because he/she has already played one with you.
That's 7 so far.
The next person plays 2 games, so that's 9.
The next person plays 1 game, so that's 10.
Then everyone has played everyone else.

So the number of games played by 5 people 1-on-1 is given by
4 + 3 + 2 + 1

So in 75 people, it would be
74 + 73 + 72 + 71 +.........+ 3 + 2 + 1

I couldn't be bothered to add them up on my calculator so i wrote a computer program to do it for me (it took no more than 10 seconds to write), and the answer is 2775.


And of course, while permutations is a much faster method, if your level of mathematics is not high enough to have studies permutations, then this technique is useful too.

Answer 2

No. It's 75*74/2.

There are lots of ways to figure this one out. The easiest way is to think of a table.
Example: if you had 6 players named a, b, c, d,e, f, g.

The table would look like this:
___a___b___c___d___e___f

a [ x ] [ x ] [ x ] [ x ] [ x ] [ x ]

b [ - ] [ x ] [ x ] [ x ] [ x ] [ x ]

c [ - ] [ - ] [ x ] [ x ] [ x ] [ x ]

d [ - ] [ - ] [ - ] [ x ] [ x ] [ x ]

e [ - ] [ - ] [ - ] [ - ] [ x ] [ x ]

f [ - ] [ - ] [ - ] [ - ] [ - ] [ x ]


The x down the diagonal are because you don't play yourself. The x above the diagonal is because you only play each opponebt once so b vs. d is the same as d vcs. b.
The total number of games played is equal to the number of boxes without an x.
If you erase everything in the above table, except the empty boxes, the table would look something like this:

[ ]
[ ] [ ]
[ ] [ ] [ ]
[ ] [ ] [ ] [ ]
[ ] [ ] [ ] [ ] [ ]

putting it togethrt with the following:

[ ] [ ] [ ] [ ] [ ]
[ ] [ ] [ ] [ ]
[ ] [ ] [ ]
[ ] [ ]
[ ]

you end up with

[ ] [ ] [ ] [ ] [ ]
[ ] [ ] [ ] [ ] [ ]
[ ] [ ] [ ] [ ] [ ]
[ ] [ ] [ ] [ ] [ ]
[ ] [ ] [ ] [ ] [ ]
[ ] [ ] [ ] [ ] [ ]

which is 6*5 = 30 and is double the number of games to be played, there fore the number of games played is 30/2 = 15.

Extend this to 75 players and you get 75*74 = 5550. Then 5550/2=2775 games.

Answer 3

You are counting games more than once (player 1 vs 2 is the same as player 2 v 1).

The proper formula is 75!/(73!2!) - basically calculating how many different combinations of 2 you can have with 75 people.

= 75*74*73!/(73!*2*1)
= 75*74/2
= 2775

Answer 4

(75-1)/2 * (75) = 2775

also, easier on the calculator you could use the nCr button.
where n = 75 and r = 2.
nCr is used for combination problems such as this, where order doesn't matter.
In this case you need to find out how many different combinations of two people you could make from a total of 75 people. Order doesn't matter because, for example, Bill plays against John is the same as John plays against Bill.
n = total # of objects in the group
r = the # of objects you are picking from the group

Answer 5

Well, i think that this probably can be considered once... My guess is 74+73+..... +3+2+1= 2775.
i may be wrong but since every student has to play 1 on 1 with every other player in the class other than himself, the first student will have 74 matches. the 2nd student will already have played against the first student.. so he will have 73 matches to play. again, the 3rd student will have already have played matches against the 1st and 2nd students. so he will have 72 matches to play...
so on and so forth...

So i think 2775 matches in all is the answer.

Answer 6

Multiply 75 X 74 = 5550 because you don't play yourself. Then divide by 2 and that equals 2775 because if you play Johnny or Johnny plays you that's the same game.

Answer 7

no, it's 74 +73+72...
Imagine the line of 75 kids. One goes down the line playing with the other 74, then the next kid starts down the line and plays 73 games (he already played with the first kid in line), and on and on and on.

Answer 8

in terms of permutations and combinations, the answer should be 75 C 2 i.e. 75! / ( 2! * 73!)
.so ans= 2775

Answer 9

there will be exactly 2690 matches.

its simple u just see how many matches does the 1st player gets with the other players,same with the 2nd 3rd.....74th and add em all up.
its the easiest way but u can also apply binomial.