Tuesday number Two

Re: Tuesday number Two --  corrected (maybe)

Alex Y

One nail. All of the piles that it is divided into are empty.

Or assuming you wanted a nontrivial answer:

One more than ten gross score, less M and fourscore.

Unless I messed up the obfuscation

Re: Tuesday number Two

Larry Barrett

I haven't decoded Alex's answer yet, but I think this is a different answer:

One more than a movie title!

Re: Tuesday number Two

Bill Earl

Your trivial answer doesn't work because 1 is not divisible by 11. (read the last line carefully)

If you divide it evenly into 11 piles, you will have none left over.

I may not understand your obfuscation, but the way I caclulate that doesn't work either.

Don't think so

Bill Earl

It may be a film I have never heard of, but a search of IMDB for that name (number) turned up empty.

Re: Tuesday number Two

Alex Y

I messed up my obfuscation; hopefully fixed now. But I don't know of a movie title that fits with my answer.

Re: Tuesday number Two

Alex Y

(read the last line carefully)

Oh, I NEVER do that!

If you divide it evenly into 11 piles, you will have none left over.

Whoops!

Re: Tuesday number Two

Dan Donaldson

vente cinco mil dos cientos y uno

s� se�or   

Re: s� se�or 

Larry Barrett

Dan's answer much simpler, but my answer also works, I think:

10! +1.

10! is way too big 

Tuesday Answer

Bill Earl

Dan was the first with a recognizably correct answer: 25,201

I'm not sure if I'm decoding it right, but I think Alex's revised answer works out to be too high.

But he didn't ask for the smallest solution

Alex Y

I agree with your solution (once Bill pointed out that I should read more carefully!).

My problem with Larry's is not the size, but how to know that 10!+1 is a multiple of 11. It may be, but I don't see how to tell that.

Re: Tuesday Answer

Alex Y

I'm not sure if I'm decoding it right, but I think Alex's revised answer works out to be too high.

Correct, and it was = 1 mod 11, because of my misreading of the problem. The correction was to my obfuscation, not to the answer. I got Don's answer, but after he did.

My attempted obfuscation was

One more than ten gross score, less M and fourscore

1+ 10 * 144 * 20 - 1000 - 4 * 20 = 27,721, which is the smallest number greater than 1, which is equal to 1 mod 2,3,4,...,and 11, the problem I read, even if it's not the one you posted

Good problem!

Re: But he didn't ask for the smallest solution

Larry Barrett

I stumbled onto my solution (10! + 1) by the straightforward way of finding a number that would satisfy the first 9 criteria (remainder of 1), and then discovered that it was also divisible by 11. My handy dandy pocket calculator has a ! key, so was easy to compute 10! = 3628800, so 10! + 1 = 3628801.

328801/11 = 329891. I have not discovered a simple way to know that 10! +1 is divisible by 11 without doing the division.

So not a very elegant solution, but it is a solution.

Actually

Dan Donaldson

More elegant than the way I did it.

How to tell if a number is evenly divisible by 11

Larry Barrett

Pondering how to know without doing the division, I Googled "rule for dividing by 11" and found an interesting web site that has simple rules for knowing if a number is evenly divisible by 2, 3, 4, 5, 6, 8, 9, 10, and 11.

Here is the rule for 11:

A number passes the test for 11 if the difference of the sums of alternating digits is divisible by 11.

So for 10!+1 = 3628801 the sum of alternating digits is (3+2+8+1)= 14 and (6+8+0)=14. Difference is 0; 0 is evenly divided by 11, so 10!+1 is, too.

Amazing what you can find on the web.