WHATS THE ANSWER

[gabe]

Consider a set of m distinct positive integers. What’s the largest integer, d,
that when divided into the m integers is guaranteed to produce at least one
pair of results with the same remainder? Explain.

[gabe]

d= m - 1? i think that makes sense

[takesix]

Do your own homework.

[gabe]

studying, not hw

[pgil]

you forgot to explain your answer though

[gabe]

"Ooooh, a sarcasm detector. Oh thats a REAl useful invention." - Comic book guy.

i used to always quote that line myself...but you have to mention how theres a sarcasm overload after he says that

[arkana]

Do you mean your set of numbers run from 1,2,3,..,m-1,m? Because the way you phrased it m sounds like the number of integers in your set.

[arkana]

The range of possible remainders go from 0 to d-1 (remainder can't be equal or bigger than d else the quotient would be 1 more). So if we want a remainder to appear more than once we would need to have more numbers than the possible number of remainders. Since the range of possible remainders (0 to d-1) contains d numbers we need to have d+1 numbers. So if our set of numbers goes from 1..m we have m numbers and d=m-1, if our set of numbers go from 0..m we have m+1 numbers and d=m.

[gabe]

theres the reasoning alright....i knew you were good for something arkana

i owe you a favor now if something like that shows up as a question

[a500lbgorilla]

"Hey, what did you get for number 6?"

"Oh, yah, I got the sum of engineering can lick my sack."

[Halv]

42.

[thenonsequitur]

42.

Yes, but what's the question?

[Halv]

42.

Yes, but what's the question? <-----------

That, my friend, is the question .

[takesix]

42.

Yes, but what's the question?

What is 6 by 9?

[jyms]

What is 6 by 9?

My rubber cell after this thread.

[takesix]

What is 6 by 9?

My rubber cell after this thread.

powned.

[thenonsequitur]

What is 6 by 9?

54?

[takesix]

What is 6 by 9?

54?

Wrong.

[thenonsequitur]

What is 6 by 9?

54?

Wrong.

Not my fault I learned math in base 10.

[jyms]

6' by 9' = 54 sq/ft

6" by 9" = 4' 6"

6 by 9 or 6/9 = .66666666666666666666666666667

or big red would say 6 by 9 is 69 which is self explanitory.

[Lukie]

seriously gabe, you're studying when you could be ballin' at 25/50 with hal or building sweaters. I'm disappointed in you.

[takesix]

What is 6 by 9?

54?

Wrong.

Not my fault I learned math in base 10.

base 13 ftw

[gabe]

seriously gabe, you're studying when you could be ballin' at 25/50 with hal or building sweaters. I'm disappointed in you.

actually i was playing 25/50 while doing this, only made 1 stack though

[spoonitnow]

d= m - 1? i think that makes sense

That's correct.

Consider the biggest case for m relative to d. If the m numbers are {d+1, d+2, d+3....d+d}, then each of these divided by d will give different remainders, namely {1, 2, 3....d}, and m = d. If m is any bigger (or d is any smaller) then you'll have two numbers with the same remainder when divided by d, so you can say d = m - 1 to satisfy your question.

[arkana]

d= m - 1? i think that makes sense

That's correct.

Consider the biggest case for m relative to d. If the m numbers are {d+1, d+2, d+3....d+d}, then each of these divided by d will give different remainders, namely {1, 2, 3....0}, and m = d. If m is any bigger (or d is any smaller) then you'll have two numbers with the same remainder when divided by d, so you can say d = m - 1 to satisfy your question.

FYP