Problem 222

[ozgur]

My shortest pipe results in two intersecting spheres. One sphere (s_n) in the middle intersects with the sphere two levels below it (s_n-2). To account for that, I move s_n along the pipe a little so that it does not intersect with s_n-2. Am I on the right track, or should the correct solution result in no such intersections?

[ed_r]

No intersections.

[axelbrz]

Hi, can anyone confirm me if the length in micrometers of the shortest pipe, of internal radius 50mm, that can fully contain 3 balls of radii 48mm, 49mm and 50mm, is 293949?

Thank you!

[stijn263]

Just putting the 3 balls on top of eachother you arrive at 294,000 micrometers. So 293,949 seems correct, but you should be able to verify this for yourself (by checking all 6 configurations)

[axelbrz]

Yes, I did it! :) But I just wanted to know if I got the concept because my answer is wrong.

I'll check it.

Thanks!

[axelbrz]

Mmm.. I'm also getting a wrong answer...

Can anyone confirm me if the shortest length of the pipe in micrometers for balls with radii 28, 31, 34, 35, 36, 37, 40, 45, 49 and 50 mm is 648649?

Thanks!

[daniel.is.fischer]

No, it can't be that short.

[daniel.is.fischer]

Hi, can anyone confirm me if the length in micrometers of the shortest pipe, of internal radius 50mm, that can fully contain 3 balls of radii 48mm, 49mm and 50mm, is 293949?

Thank you!

No, it's 293933.

[x10]

I'm sorry to be reiterating the topic, but could anyone please post their answer for balls of sizes 40, 41... 50?
I get 983801.638816

[daniel.is.fischer]

Too close to the problem's parameters to post the correct value, but yours is too high, the correct value is 981xxx.yyyyy

[mirzauzairbaig]

Can anyone please list any particular basic topics that I need to go through to work on this problem ?

[TripleM]

The best part about Project Euler is that you need to come up with the answers all by yourself, you won't be finding hints online

Let's just say that a brute force approach doesn't need to check all N!/2 possibilities.

[daniel.is.fischer]

Let's say a brute force approach is supposed to not be a good idea. Look at the function that gives you the length or saved length locally. It has a property which lets you find the optimal arrangement quite easily (assuming what you're studying is mathematics or has a large mathematical component, like physics).

[TripleM]

Or that. Either way gives a fast answer

[jui-feng]

I'm sorry to be reiterating the topic, but could anyone please post their answer for balls of sizes 40, 41... 50?
I get 983801.638816

It's kind of funny I was getting exactly the same (invalid) response for 40-50. It seems like we both made the same mistake that resulted in the same result, I only had some more decimal places (double precision).

Anyway, I solved it now.

[yourmaths]

One small quibble over the rounding of the final answer here. Let's say the answer to the problem is 123.4 micrometres. Rounding this (down since 0.4 < 0.5) we get 123 but this is no longer the shortest pipe since the sphere on top is now 0.4 micrometres above the top of the pipe. So my interpretation would be that the answer should be rounded up in all cases, giving 124, which was not accepted, but 123 was.

[DJohn]

One small quibble over the rounding of the final answer here. Let's say the answer to the problem is 123.4 micrometres. Rounding this (down since 0.4 < 0.5) we get 123 but this is no longer the shortest pipe since the sphere on top is now 0.4 micrometres above the top of the pipe. So my interpretation would be that the answer should be rounded up in all cases, giving 124, which was not accepted, but 123 was.

But that is not what the problem is asking for. What you're doing is finding the shortest integer length that satisfies the conditions. The problem is asking you to find the shortest length (which is not necessarily an integer) and then to round it to the nearest integer. That's a different thing. There's nothing in the problem statement that suggests that the rounded number has to meet any conditions other than being the closest integer to the shortest length.