Problem 155

[viv_ban]

Can anybody please confirm me if the values D(4) = 15 and D(5) = 35 are correct.
thanks in advance.

[Tommy137]

Yes, they are correct.

[viv_ban]

Thanks Tommy. I really cannot understand the problem with my algorithm. Is D(10) = 2491.

[Tommy137]

Unfortunately, it's wrong

[Schwein]

I don't get it either...
Is it wrong to think, that the only new capacitor combinations are the ones from the previous, with max number of capacitors, + a series and a paralel with a new 60 microfahrad capacitor?
ex

if we have 2 2 capacitor combinations, then there will be 4 extra in the next, and 8 extra in the next and so on?

I cannot imagine how else a combination would be made, but then my D(5) = 31, and i don't see where the 4 extra comes from

[jaap]

I cannot imagine how else a combination would be made, but then my D(5) = 31, and i don't see where the 4 extra comes from

Hint: 5 = 1+4 = 2+3
Remember also that we only care about the different values - some values can be made in several completely different ways, so that is another reason why it won't be a simple doubling sequence.

[Schwein]

I had the part covered, that some values might be equal(turned out none of them were, when i just added one in series, and one in paralel, for each combo), the only thing i don't understand, is why that does not give me all the different combinations makeable...

[Lord_Farin]

the only thing i don't understand, is why that does not give me all the different combinations makeable...

How about combining larger, 'composite' capacitors in series or parallel? (This is what hk meant above as well)
Think about $1 = \frac1{1+1}+\frac1{1+1}$.

[Schwein]

Ahhhhh, thank you were much the both of you, I see now where my logic fails ^^

[Erf_Erf]

It seems I can't get it right... I get the correct results for D(4) and D(5). Then D(6) = 76 and D(10) = 2147. Are these values correct?

[mpiotte]

It seems I can't get it right... I get the correct results for D(4) and D(5). Then D(6) = 76 and D(10) = 2147. Are these values correct?

No.

[Erf_Erf]

I just found the annoyingly trivial and almost invisible mistake in my code, and finally got the correct answer.

[DeKlod]

Hi all,
Could I ask for two pieces of input here:
1) D(13) is a 5-digit figure starting with a 4 and ending in an even digit - is that correct?
2) I'm using float values in C and my suspicion is that my solutions turns out wrong because of a precision issue. I've tried (long) double but the result is no more convincing. Should I try to go for the alternative of defining and manipulating fractions (as Wodehouse would have said: I've just had a look at what my mind is doing, and it turns out: it boggles!) or should I rather look for something else - my choice of value for the capacitance for example.
Cheers,
Claude

[Jochen_P]

Claude,

to answer your first question:
D(13) is indeed a 5-digit figure but it starts with 3 and ends with an odd digit.

hth
Jochen

[DeKlod]

Right, back to the drawing board then ...
Thanks for getting back though!

[DeKlod]

Right, got there in the end, although the program takes about 40 seconds to come up with the answer...
Thanks for the help again!
Claude