Problem 086

[thundre]

Thanks.
I'm still a bit baffled why:
"there are exactly 2060 cuboids for which the shortest distance is integer when M=100," doesn't raise any thorn.

Should be: "there are exactly 2060 cuboids for which the shortest distance is an integer when M=100"

Most people probably inserted the article subconsiously, without realizing it was missing.

IMHO "shortest distance is an integer" is less clumsy than "shortest route has integer length".

[Marcus_Andrews]

Should be: "there are exactly 2060 cuboids for which the shortest distance is an integer when M=100"

Most people probably inserted the article subconsiously, without realizing it was missing.

IMHO "shortest distance is an integer" is less clumsy than "shortest route has integer length".

I agree with you, but I don't think hk likes using "an" here (although I'm not sure why) -- same reason why he didn't change the earlier case to "an integer."

[hk]

Look good into the proposed sentence for the first case:
"The shortest route is not always an integer"
A route cannot be an integer, at least not in my opinion.
A route is a path you follow. One of the properties it can have is its length.
I think my criticism about that proposed sentence has a deeper meaning than peculiarities of some language or other.

[frogjg2003]

Do your results up to M=9 match what DDgeva and Jaap posted above?

I'm getting 14.

[thundre]

Do your results up to M=9 match what DDgeva and Jaap posted above?

I'm getting 14.

I'm copying the list from an earlier post. Check which one you're missing. Maybe you can fix your solution if you know exactly where it fails.

Code: Select all

    3 2 2
    3 3 1
    4 2 1
    6 4 4
    6 5 3
    6 6 2
    6 6 5
    7 5 5
    7 6 1
    8 3 3
    8 4 2
    8 5 1
    8 5 4
    8 8 7

[frogjg2003]

I'm missing 665, 755, 761, and 854.
I checked 665, and the three "shortest paths" are 12.53, 12.53, and 13. So the shortest path is not 13. As I understand the problem, this should not be included.

[rayfil]

I'm missing 665, 755, 761, and 854.

I would strongly suggest you read this thread from the start.

[frogjg2003]

I'm missing 665, 755, 761, and 854.

I would strongly suggest you read this thread from the start.

I have and I'm still not sure what's wrong.
Is 665 a solution or not? I'm getting that it's not because there are shorter paths than 13, but it was included in thundre's list, so I'm not sure.

[rayfil]

but it was included in thundre's list

Did you check where he took that list??? And the subsequent posts?????

[thundre]

but it was included in thundre's list

Did you check where he took that list??? And the subsequent posts?????

Sorry. I thought it was a correct list, because I didn't check those posts either.

[frogjg2003]

Since I can't get a straight answer, I'm posting my results to M=15

Code: Select all

3 2 2
3 3 1
4 2 1
6 4 4
6 5 3
6 6 2
8 3 3
8 4 2
8 5 1
8 8 7
9 6 6
9 7 5
9 8 4
9 9 3
12 3 2
12 4 1
12 5 4
12 6 3
12 7 2
12 8 8
12 9 7
12 10 6
12 11 5
12 12 4
15 4 4
15 5 3
15 6 2
15 7 1
15 10 10
15 11 9
15 12 8
15 13 7
15 14 6
15 15 5

From this I get:

Code: Select all

5 3
10 14
15 34

Are these right or not?

[frogjg2003]

bump for an answer

[thundre]

You're missing "12 8 1".

[Loers]

this is the list that i got for M=19
http://pastebin.com/ENb7czzM

is there sth wrong with it ?
I tried to look throught the comments to see the complete list but couldn't find that,,

thanks in advanced ^_^

[rayfil]

As stated in the problem description:

up to a maximum size of M by M by M

Which means you could have a cuboid as large as 19x19x19 when M=19 (such as a 10x14x18).

[Loers]

oh sorry I mean M=9

[TheEvil]

oh sorry I mean M=9

Actually row (1 6 7 sol1 : 10.000000 |) is not a good answer, since the shortest paht is sqrt(98). And that's not the only bad row.

[garyp]

The other thread is a mess of semantics and word disputes so I'm starting a new one. The accepted answer does not match mine so here I am. I have used my algorithm to compute correctly:
99, 1975
100, 2060
in accordance with the example provided. My number that results in 1,000,000 is nowhere near the official answer. Using some predictive analysis, you can guess where my answer falls based on this chart. Do you have any pointers for someone that correctly arrives at the example but whose following results look like this: http://i.imgur.com/eFHHM.png
Thanks

[TripleM]

If your answer lies close to where that graph suggests, then your answer is too low. That means your value has less than a million solutions, so if you write some additional code that ensures each of your million solutions is valid and unique then you'll find your problem.

[hk]

@garyp.
It's not up to you to decide a new topic must be created.
So I merged the two topics.
The reason for that is that it isn't helpful to have more than one thread for a problem.
Everybody after you would have to scan both threads which makes this forum yet more messy.
(And thanks for having forced me to do some moderating)