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May 28, 2007

May's math problem

What is the lowest number between 678,000 and 679,000 that is a multiple of 6,7 AND 8, but doesn't have a 6,7, or 8 in the lower place values?

Example:678,048 is divisible by both 6,7, and 8, but has an 8 in the ones place.

No rewards, except that you know you used your brain. Hop to it.

***Update***
Twenty minutes after posting it, a really cute and obviously smart guy in Arizona solved it. Only look in the comments once you've got your answer!

Posted by G at May 28, 2007 06:18 PM

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for ($i=678000; $i if ($i % 6 == 0 && $i % 7 == 0 && $i % 8 == 0) {
if (ereg('[0-9]{3}[^678]{3}', $i)) {
echo number_format($i)."\n";
break;
}
}
}


678,552

Hooray!

Posted by: Adam at May 28, 2007 07:49 PM

I definitely don't have enough fingers and toes to answer that question!

Posted by: Seth at May 28, 2007 10:02 PM

Oh Adam is a smarty pants!

Posted by: homer at May 28, 2007 10:31 PM

What the hell did he just do up there?

Posted by: Doug at May 28, 2007 10:55 PM

%the same thing, but matlab
for i=678000:679000
if (rem(i,6)==0 & rem(i,7)==0 & rem(i,8)==0)
i
else
i=i+1;
end
end
***

-> 678 384 !!!!

eh?
hugs from méxico

Posted by: Daniel at May 29, 2007 01:15 AM

We were allowed to let a computer do the work???

I spent an hour on paper with those old rules "divisible by 6 means divisible by both 2 and 3", "divisible by 3 if the sum of the digits is divisible by 3", etc etc.

And with a shell script, no less.

Tabarnac de crisse!

Posted by: Jim (The Canuck One) at May 29, 2007 04:35 AM

A multiple of 6,7, and 8 has to also be a multiple of 2*2*2*3*7 = 168. So we start with the lowest multiple of 168 in that range, then by adding 168 again and again we just have to observe the last three values. A little bit of a brute forced method, admittedly, but not too bad considering the narrow range (there are only 6 multiples of 168 between 678,000 and 679,000)

678,000 / 168 = 4035.7...
round up to 4036

4036*168 = 678,048 - no, but it's a starting point (also guess we could've used G's example :)

and now we keep adding 168

678,216 - no
678,384 - no
678,552 - yes!

Posted by: Carl at May 30, 2007 06:54 AM

This is why I am an artist, as I don't even know what "lower place values" means.

Posted by: Scott at May 30, 2007 09:42 AM

my head hurts. and i had the answer in front of me.

Posted by: chris at May 30, 2007 12:14 PM

Math is better left to the experts... I'll take the questions about Battlestar Galactica or Merman show tunes...

Posted by: Todd HellsKitchen at May 30, 2007 04:47 PM