A place to air possible concerns or difficulties in understanding ProjectEuler problems. This forum is not meant to publish solutions. This forum is NOT meant to discuss solution methods or giving hints how a problem can be solved.
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On the image above, both inside and outside "rim to rim" over then same cup are present.
I don't see why it should be forbidden (it is said "Ck+2 or Ck-2" and "or" is inclusive by default?)...
But this gives me too many different stacks for N=8 (I drew and checked all of them).
Can you clarify on this matter?
If you look at the two diagrams for rim-to-rim it's reasonably clear that the green 3 covers substantially more than half of the top orange edge, and the covered top of the blue 4 is well more than half of the base of the yellow 2, while your diagrams have exactly half in both cases.
I modified my code, so now, the shapes are identical to the ones of the PE page for the problem.
Especially, the "rim to rim" 3 over 1 match exactly!.
Well, this eliminates some stacking: if you have both inside and outside "rim to rim" ove a cup^, you can't stack anymore a third cup between the two!
But, this does not prevent to stack both inside and outside "rim to rim" over a cup.
Then my need for clarification is still pending.
@SNAIL-ERATO: Thanks, this is a great catch, and you are correct that the diagrams make it look like stacking both $C_{k-2}$ and $C_{k+2}$ rim-to-rim on top of $C_k$ should be possible. However, for this problem we assume that one cannot do so.
The problem statement has been updated to clarify.
Ok.
When, i don't accept both inside and outside "rim to rim" over a cup, i get now the correct answer for N=8.
So, i continue to try to solve the problem assuming this was intended.
Anyway, i don't regret the time spent at making those nice drawings :
Topic closed.
I hesitated to post this one, because i don't really like to "Jouer les mouches du coche" as we say in French.
But i do think that it would be worth mentioning that the configuration $C_{k+2}$, $C_{k-1}$ on the top of $C_k$ is not authorized too.
I don't think that it is strictly forbidden by the rules, and, depending on the exact shape of the cups, it may or may not be physically possible.
But we know little enough about the exact relative proportions of the different parts of the cups.
And, as the problem is stated, we have to zoom on the examples given and measure them carefully to conclude that it is not!
I am old enough to have learned a lot of Euclidean Geometry at school (and liked it so much!). At the time, in the 60ies, no figure was ever given with the statement of a problem.
The first task we had to do was to build the figure from the instructions given ahead of the questions.
More, our teachers warned us repeatedly that a figure could be deceiving, should never be trusted totally and, so, was just a help for the reasoning!
Anyway, I shall never thank enough the Project Euler team for the long hours of pleasure they give to me with such amazing riddles.
First, being at the crossroad of Math and Algorithm, they seem to have been designed especially for me: a, now retired, Programming Engineer (and Math lover!).
Second, at 548 problems solved today, the remaining ones are becoming more an more challenging to me (being a Math lover does not make me a genius LOL): so i have surely enough to play with, until my last breath!
Best regards.
Thanks for flagging this as well. For now though, we'll leave the phrasing as it is as the problem is already quite wordy. If we see people misinterpreting the problem in that way then we can reconsider.
