Problem 173 & 174

[ed_r]

Re stats: it would be nice to know, for each problem, the number of people that were (eventually) successful as a proportion of the number of people that had submitted any attempt at an answer. But I seem to remember Colin saying something about the database being too big now, so I don't suppose that's going to be possible for the PE stats page. Oh well.

[daniel.is.fischer]

Would be interesting, but to enter an answer, be it correct or not, you must have understood a fair bit about the problem in many cases. Okay, a lot are brute-forceable in less than two days, but e.g. #152 is way beyond that, would take a couple of years. And 133 is even theoretically unbrute-forceable, you must understand enough of the theory that the only question is whether you think a couple of minutes more to write a programme that returns the answer in a second or write one which runs perhaps 5 minutes.

@joshbowman205: Yes, it seems most people start with the easy ones (I started with the ones I found most interesting), but even so, imagine you have solved 70% of the problems and find the rest is way beyond your education. We don't want to tell such people "Too bad, no more fun for you here". We want to lead them deeper into the beautiful world of mathematics. On the other hand, we don't want to bore people like you much either, we're trying to find the right balance. All help welcome.

[Zell]

I feel rather silly posting this, but... the language in 173 is confusing me. I'll try to ask for clarification without asking for help (especially since I suspect the problem is not terribly hard):

With one-hundred tiles, and not necessarily using all of the tiles at one time, it is possible to form forty-one different square laminae.

What exactly is the restriction being placed on the laminae? I took it to mean 'any lamina that uses up to 100 tiles' but now I am not so sure. The term 'at one time' is a bit vague. Perhaps 'any collection of laminae whose tiles add up to precisely 100'?

[ed_r]

There are 41 laminae that (each) use 100 or fewer tiles.

The question is then: how many laminae are there that (each) use 1000000 or fewer tiles?

I got confused at first, too, thinking that the question wanted me to produce lots of laminae all at the same time (so maybe you can get through, oh I don't know, 1000 laminae before you run out of tiles). But the picture in the question makes it clear that I was wrong.

[Zac256]

I think it might be useful to note that there is one and only one hole in a square laminae. Without this it seems like the following might be a valid solution... It is 1. Symetrical. 2. Square outline. 3. Missing center square.

1111111
1011101
1111111
1110111
1111111
1011101
1111111

[daniel.is.fischer]

"We shall define a square lamina to be a square outline with a square "hole" so that the shape possesses vertical and horizontal symmetry."
Isn't the singular article clear? If multiple holes were allowed, wouldn't one have to say 'with one or more square holes'?
To me (not a native speaker, though) it seems unambiguous. What do the english say?

[joshbowman205]

Its a little tricky at first but yes it is unambiguous. Changing it to "one square hole" is preference

[daniel.is.fischer]

But would remove all possibility of misunderstanding, so I think it's good.

[LeeBreisacher]

I know I'm not supposed to discuss unsolved problems, or ask for help, but I'd like to know what my options are. Here's the situation: I have studied problem 173, written a simple Java program to solve it, studied it some more, thought about it at length, and I cannot see what's wrong with my solution. So, I'm wondering if any of these things are possible/allowed:
1. I could post my answer for 1000 tiles, 10000 tiles, etc. and see if it matches others that have solved it correctly. (Yes, my solution does produce 41 for 100 tiles).
2. Strike up a private email conversation with someone that has solved it correctly -- not to give me the answer, but just to see if I'm on the right track or try to discover where my thinking might be faulty.
Thanks,
Lee

[rayfil]

You could send me a PM (Private Message). Can't promise an immediate answer though.

[LeeBreisacher]

Never mind -- I figured it out. Thankfully for my sanity, my algorithm was correct, I just missed an int overflow error.

Thanks,

Lee

[stijn263]

It is now the intention of the Project Euler team to rotate the difficulty of new problems through an easy-medium-hard-medium- cycle

so problem 175 is considered to be of medium difficulty?

[daniel.is.fischer]

We weren't sure, problem 169 seemed much easier than we expected. Originally it was considered hard (not terribly hard), but we changed it a bit (now it can be done with pencil & paper in less than one minute -- given you know how). Time will tell how wrong we were. Seems you'd not rate it as easy, would you?

[stijn263]

definately not easy, but after problem 169, it wasn't hard either, at least, that was my experience. a medium difficulty problem fits nicely into the "Project Euler teams' intention" i guess

i think so many users have solved problem 169 because the recursion isn't that hard to find, and there are also a lot of other approaches that can be used. problem 175 can be considered hard if one hasn't solved 169 yet i think.

[hk]

definately not easy, but after problem 169, it wasn't hard either, at least, that was my experience. a medium difficulty problem fits nicely into the "Project Euler teams' intention" i guess

i think so many users have solved problem 169 because the recursion isn't that hard to find, and there are also a lot of other approaches that can be used. problem 175 can be considered hard if one hasn't solved 169 yet i think.

That's why we put them in that order. We could also have restricted ourselves to #175 only but that would have been less than half as nice. Do you see now why developers notes are not always a good idea?

[ed_r]

Why do you assume that the dev notes for #169 should give everything away? No-one said they should be comprehensive. It would be naive of a developer to release notes that killed off the possibility of interesting follow-on problems.

[stijn263]

That's why we put them in that order. We could also have restricted ourselves to #175 only but that would have been less than half as nice.

perhaps it would be nice to add a note to problem 169 and 175, so people know they'll have more success trying 169 first. something like:

NOTE: This problem is an easier version of problem 175; it is advised that you solve this one first.

NOTE: This problem is a difficult version of problem 169.

[drwhat]

I was curious if anyone who had solved this could PM. I have solution for N(n) for 1 <= n <= 20. My N(15) matches 832 correctly but my summation of 1 to 10 seems off. I was wondering if could PM someone that list to see how far off i was.

[Marcus_Andrews]

Feel free to PM me

[jdorje]

Problem 173 seems pretty ambiguous. What does "not necessarily using all of the tiles at one time" mean? This is the opposite of the "unique" tiling given in the example? Why make the example show one thing then make the problem something, not just more complicated (that's normal), but with no precise definition?