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# Help! A remainder is chasing me

Best Answer normdeplume , 19 September 2007 - 07:23 PM

My answer is below, is this the answer you were looking for or is there a lower one?

Spoiler for solution

Just because your voice reaches halfway around the world doesn't mean you are wiser than when it reached only to the end of the bar. Go to the full post

67 replies to this topic

### #11 kafka

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Posted 22 January 2008 - 03:48 PM

I'de write a computer program in C# that has 10 ifs and get to the number very quickly, but without the mathematic understanding, and for that I thank you guys
• 0

### #12 octotus

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Posted 30 January 2008 - 09:45 PM

wrote a simple script - the smallest number is 2519.

here is my way.

\$solution = "F";
\$x=0;
while(\$solution eq "F")
{
\$x++;
\$flag=0;
for(\$i=1;\$i<10;\$i++)
{
\$j=\$i+1;
\$y=\$x%\$j;
if(\$y != \$i)
{\$flag=1;}
}
if(\$flag==0)
{
\$solution="T";
print \$x,"\n";
}
}
## it is perl.
• 0

### #13 Sanjurjo

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Posted 31 January 2008 - 02:11 AM

wrote a simple script - the smallest number is 2519.

here is my way.

\$solution = "F";
\$x=0;
while(\$solution eq "F")
{
\$x++;
\$flag=0;
for(\$i=1;\$i<10;\$i++)
{
\$j=\$i+1;
\$y=\$x%\$j;
if(\$y != \$i)
{\$flag=1;}
}
if(\$flag==0)
{
\$solution="T";
print \$x,"\n";
}
}
## it is perl.

That seems to take more knowledge of the working mathematics than the other mathematics solutions provided. Guess it just goes to show that math and logic are very much the same animal.
• 0

### #14 freyr

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Posted 03 February 2008 - 12:40 AM

Actually any number (2520 * K) - 1 where k is any positive integer has these properties
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### #15 Larry

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Posted 13 February 2008 - 05:22 AM

This problem is simple. All you have to do is find the least common multiple of 2,3,4,5,6,7,8,9, and,10. Then you subtract 1 from that number so that it is not divisible by anyone of those numbers. the number is 2519
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Posted 14 February 2008 - 07:21 PM

Can also just use XL VB...took 30 secs...just use "mod" to check the remainder, and see if they add up to 45...

Sub xxxx()

For i = 1 To 100000

Cells(1, 3) = i

If Cells(10, 1) = 45 Then
Exit For
End If

Next i

End Sub
• 0

### #17 bonanova

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Posted 15 February 2008 - 06:09 AM

I'm curious ... any of you programmers ever use APL?
It's interpretive, very useful, and very ancient.
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The greatest challenge to any thinker is stating the problem in a way that will allow a solution.
- Bertrand Russell

### #18 Duh Puck

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Posted 15 February 2008 - 07:55 AM

I'm curious ... any of you programmers ever use APL?
It's interpretive, very useful, and very ancient.

After reading the Wikipedia entry and looking at those samples, I'd have to agree that it looks really cool, and totally impractical for any of the work I do. I like the poem at the bottom of the page:

'Tis the dream of each programmer
Before his life is done,
To write three lines of APL
And make the damn thing run.

Perhaps I can make some time on the weekends to learn an arcane, remarkably dense language that I'll never use in real life for the purpose of solving math problems with less code. That I say this in all seriousness is probably a rather sad commentary on my social life.
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### #19 Aatif

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Posted 15 February 2008 - 08:28 AM

I just found a number with an interesting property:

When I divide it by 2, the remainder is 1.
When I divide it by 3, the remainder is 2.
When I divide it by 4, the remainder is 3.
When I divide it by 5, the remainder is 4.
When I divide it by 6, the remainder is 5.
When I divide it by 7, the remainder is 6.
When I divide it by 8, the remainder is 7.
When I divide it by 9, the remainder is 8.
When I divide it by 10, the remainder is 9.

It's not a small number, but it's not really big, either.
When I looked for a smaller number with this property I couldn't find one.

Can you find it?

No need of a brute force method...
Spoiler for Elegance

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Posted 15 February 2008 - 02:32 PM

2519
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