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Geek Culture / Math Problem

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MartinS
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Joined: 15th Dec 2005
Location: Rochester, NY
Posted: 18th Oct 2007 23:58
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Hi all,

Here's a little math problem that I er, hoped you'd solve. Of course this doesn't have anything in the least to do with my homework.



The athletic committee is going to have an annual awards banquet. They find that whether they seat 3 players at each table or 4, there is going to be one player left over. But, with 5 player at each table, all the player can be seated. If there will be between 30 and 100 players at the banquet, how many will be there?




Post work too, please.

MS

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Diggsey
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Posted: 19th Oct 2007 00:23
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The answer is 85
The working... This is where the programmer has the advantage


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Mr Tank
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Posted: 19th Oct 2007 00:24
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It leaves a remainder of 1 when divided by 3 or 4, so it'll be a multiple of 12, plus 1. ie 12n+1, n integer.

The number of players must therefore be odd, so the number will end in 5 (not 0)- note that a multiple of 5 ends in a 0 or a 5. So let's look for a multiples of 12, between 30 and 100, ending in 4.

36,48,60,72,84,96

There are 85 players.

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MartinS
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Posted: 19th Oct 2007 01:37
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Thanks for the help, guys. Quick question though: why must it be a multiple of twelve? I see the relationship between the 3 and the 4 and the 12, I just don't see why it is so. But other than that, thanks again.

MS

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demons breath
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Posted: 19th Oct 2007 02:03
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Because regardless of whether you divide by the 3 or the 4, the remainder will always be one, therefore you are only looking at numbers which are multiples of both.

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Mr Tank
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Posted: 19th Oct 2007 02:03
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The number of players, less one, must divide into 3 or 4 with no remainder.
If a number is a multiple of both 3 and 4, it must also be a multiple of 12. This may not be instantly obvious. If you can look at the remainder of divisions by 3 and 4, the remainder 0/4 is 0, of 1/4 is 1, so the remainders of 0,1,2,3,4,5,6,7,8 when divided by 4 go

0,1,2,3,0,1,2,3,0..

Similarly for 3. -

0,1,2,0,1,2,0,1,2,..

The only time the remainder is zero in both cases is for multiples of 12.
It is not true to say this for all numbers though- eg if you want a number that divides exactly into 3 and 12, it's multiples of 12 again, not multiples of 3*12=36. Look up prime factorisations...

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Aaron Miller
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Posted: 19th Oct 2007 02:13
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The answer is 42. The work? Well that's a known fact! 42 is the answer to life, the universe, and everything.


Cheers,

-naota

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MartinS
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Posted: 19th Oct 2007 02:19
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Quote: "42 is the answer to life, the universe, and everything."
Well, obviously! I really don't see why you other people didn't follow this well know fact.

Seriously though, thanks (again).

MS

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demons breath
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Posted: 19th Oct 2007 02:22
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Quote: "The answer is 42. The work? Well that's a known fact! 42 is the answer to life, the universe, and everything"


Man, now I feel like a fool for overlooking that

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