george

ok never mind manually saved to pdf now, but weird I couldn't find that btn

i bookmarked chat conversation but can't find UI to find the bookmark

And weirdly this chat shows my rep from another stack exchange site, maybe it is a bug.. Anyway thanks and good night.

i mean see something in chat tomorrow

but I am not sure

@TedShifrin My main problem remains the N-1 term, somehow I couldn't follow your points where you explained it that is why I hope tomorrow I can see something there

@TedShifrin Hmm.. Ok I hope tomorrow when I come back to this chat it will be more clear for me. if you write an answer it will be even better potentially for others. Either way, thanks and good luck!

That's my problem currently :)

@TedShifrin " are in $N-1$." Why in N-1?

@TedShifrin Anyway if you don't feel like explaining anymore it is OK too, no big deal

@TedShifrin Ok I will try. But why is there dark in my room? First step 4 hours it is lit right? When the fourth hour ends I can already use new candle obtained from burning first two candles. Then I can use candle obtained by burning 3rd and 4th candles. And then I can create final new candle and immediately burn it

@TedShifrin Do you think you can do that?

@TedShifrin Sorry it is getting late here and I need to go to bed soon :( (due to work) It will be best I think if you write up an answer which conceptually explains and justifies use of N-1 and M-1

@TedShifrin in which my step is the error?

@TedShifrin When are N-1 already burned? after which step?

@TedShifrin why N-1 is used in nominator, that part I still can't follow :( sorry.

@TedShifrin Not sure what you mean

by N-1

@TedShifrin I thought by -1 he was referring that in the FINAL moment you have one unused burnt candle left

@TedShifrin Does N-1 make sense too?

@TedShifrin How did you see the formula from examples, didn't you just assume "k+[(k-1)/(m-1)]" in the induction and you assumed that because the books explanation said so, wasn't that the case?

That's not how you write explanations for people who you want to teach programming via puzzles

@TedShifrin Problem is cool but I was dissapointed by explanation

because of that :)

I threw out the book actuallyu

@TedShifrin I see at least I will not be suffering by thinking I was too dumb that I didn't realize how from this books explanation the solution followed

@TedShifrin "Well known argument" now you mean the books solution is clear to you?

@Jakobian yes that's a coincidence or how it is called :)

@TedShifrin i can find authors email in case you are interested

@TedShifrin no abou programming puzzles but due to the nature of solution i thought posting here

In my country

Author is coach of programming olympiad team

laterna.ge/?cat=98&show=18935

@TedShifrin sadly i dont think it is in english

@TedShifrin nah the first one didnt illuminate me either :)

@TedShifrin yeah i thought so my math got rusty, need to lookup complete induction. Anyway feel free to write up an answer too, maybe will be useful for someone else in future

@TedShifrin "Now check that with $f(k,m)=k+[(k-1)/(m-1)]$" -- where did this come from?

@TedShifrin that was my problem I wanted to justify usage of n-1 and m-1 ... i will look at your solution.

I mean initially i was surprised

@TedShifrin didn't try examples I was merely a bit angry that author just gave that brief explanation as solution. And i was surprised why i could not see how the solution directly flowed from his explanation

In above comment

There is problem in math education often things are not well explained to students, also in response to Jaakko above. I have similar problem above, there was solution in book which itself was unclear, see my link

I would appreciate some help on this Post:math.stackexchange.com/questions/4728916/…, so far haven't got satisfactory answer :(

I will look into this tomorrow thanks for trying

In other words i want a proof why your approach works instead of plugging in concrete numbers as you did :) how the author arrived at the solution of (n-1)/(m-1).

Let's follow like this. 1) You burn N candles and get N hours. 2) Now you have N burnt candles 3) Now you take out one burnt candle for some reason. 4) You have N-1 burnt candles now and you divide them on M-1 and get say H 5) Now you have H new candles and also one burnt candle from step 3. So what ? How do you proceed now?

"because of the divisbility condition, you can get that it is in fact an equality by following the argument above."- why divisibility implies equality? no this is not advanced book :(