## Problem 713

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Junglemath
Posts: 54
Joined: Fri Sep 20, 2019 1:25 pm
Location: Minsk

### Problem 713

https://projecteuler.net/problem=713

Are the N fuses split up between the house and the shed?

Must he choose all the working fuses in order for the heat to work? So in the second example, if he has 8 fuses and 4 of them are working, are we looking for the smallest number of combinations of fuses so that he is guaranteed to have turned on the 4 working fuses?

mdean
Posts: 165
Joined: Tue Aug 02, 2011 2:05 am

### Re: Problem 713

I believe the N fuses are replacements. The only circuit has 2 fuses in series. Choose 2 replacements and, if both fuses are good, there's a closed circuit and everything works. Otherwise, there's no power. He keeps trying a different pair until he finds a pair that works.

Junglemath
Posts: 54
Joined: Fri Sep 20, 2019 1:25 pm
Location: Minsk

### Re: Problem 713

mdean wrote:
Mon Apr 27, 2020 6:13 am
I believe the N fuses are replacements. The only circuit has 2 fuses in series. Choose 2 replacements and, if both fuses are good, there's a closed circuit and everything works. Otherwise, there's no power. He keeps trying a different pair until he finds a pair that works.
I don't follow.

mdean
Posts: 165
Joined: Tue Aug 02, 2011 2:05 am

### Re: Problem 713

From https://en.wikipedia.org/wiki/Series_an ... l_circuits
In a series circuit, every device must function for the circuit to be complete. If one bulb burns out in a series circuit, the entire circuit is broken.
From this problem:
The electrical system uses two fuses in series,... For the heating system to work both fuses must work.
For the easiest given example, there are 3 fuses and 2 work. Start by inserting fuses 1 and 2 into the circuit. If this fails, either fuse 1 or fuse 2 was blown and a new pair has to be tested. If T(3,2)=3 as written in the problem, he can find a pair that works in at most 3 tries.

Junglemath
Posts: 54
Joined: Fri Sep 20, 2019 1:25 pm
Location: Minsk

### Re: Problem 713

mdean wrote:
Mon Apr 27, 2020 7:18 am
From https://en.wikipedia.org/wiki/Series_an ... l_circuits
In a series circuit, every device must function for the circuit to be complete. If one bulb burns out in a series circuit, the entire circuit is broken.
From this problem:
The electrical system uses two fuses in series,... For the heating system to work both fuses must work.
For the easiest given example, there are 3 fuses and 2 work. Start by inserting fuses 1 and 2 into the circuit. If this fails, either fuse 1 or fuse 2 was blown and a new pair has to be tested. If T(3,2)=3 as written in the problem, he can find a pair that works in at most 3 tries.
Right. I guess I don't see the significance of the fuses being split between the house and the shed. I'm imagining a total of N light switches, of which some number <= N work, and he needs to flip all of the working switches for the heat to work.

Is this accurate?

LilStalker
Posts: 73
Joined: Thu Nov 03, 2016 4:32 pm

### Re: Problem 713

Im going to give you an analogy to the problem so that things might be clearer for you. If moderators find this post inappropriate, feel free to remove it.

Suppose you have N batteries, m of them are working and N-m are not working. Now you have an electronic device into which you have to insert 2 batteries. If both of the inserted batteries are working, the device will work too.
You start putting 2 batteries at a time into electronic device by using some strategy. What is the minimal number of tries that will guarantee that the device is working?

Junglemath
Posts: 54
Joined: Fri Sep 20, 2019 1:25 pm
Location: Minsk

### Re: Problem 713

LilStalker wrote:
Tue Apr 28, 2020 8:00 am
Im going to give you an analogy to the problem so that things might be clearer for you. If moderators find this post inappropriate, feel free to remove it.

Suppose you have N batteries, m of them are working and N-m are not working. Now you have an electronic device into which you have to insert 2 batteries. If both of the inserted batteries are working, the device will work too.
You start putting 2 batteries at a time into electronic device by using some strategy. What is the minimal number of tries that will guarantee that the device is working?
Expand

LilStalker
Posts: 73
Joined: Thu Nov 03, 2016 4:32 pm

### Re: Problem 713

I think you are thinking under wrong assumptions here. You know nothing about the fuses/batteries initially. For example you pick fuse number 1 and you test it together in pair with every other fuse and in none of the cases the heating system works. That means, that the fuse number 1 is definitely bad. Of course you can do better but this is just an example. You have a set of fuses and you have no clue about them. You only know how many of them work. Now you need to find out which (or just which 2 work).

hk
Posts: 10811
Joined: Sun Mar 26, 2006 10:34 am
Location: Haren, Netherlands

### Re: Problem 713

@Junglemath:
If you think you have formulated a solution you can test it out on the given examples. Don't post one in the hope it will be correct.
PS i've removed your (wrong) assumption.

For the time being I think there has been enough here.

Junglemath
Posts: 54
Joined: Fri Sep 20, 2019 1:25 pm
Location: Minsk

### Re: Problem 713

hk wrote:
Tue Apr 28, 2020 8:05 pm
@Junglemath:
If you think you have formulated a solution you can test it out on the given examples. Don't post one in the hope it will be correct.
PS i've removed your (wrong) assumption.

For the time being I think there has been enough here.
I find it ironic that you are accusing me of posting spoilers/fishing for answers when I have been the one to report posts in the past that had any chance of containing a spoiler. I simply replied to a question posted by LilStalker, and just to be safe, I used spoiler tags.

Anyway, the whole point of this part of the site is to clarify problems whose formulation is cryptic. Based on my questions you can see that I do not understand what is being asked in this problem, so I cannot really "test" anything. My goal is to understand the question, not to look for the answer.

Thanks

hk
Posts: 10811
Joined: Sun Mar 26, 2006 10:34 am
Location: Haren, Netherlands

### Re: Problem 713

The problem was that you posted something you thought was a solution.
In my opinion you have been served enough.

Actually Lilstalker didn't ask you a question.
Lilstalker translated the question of the problem to the translation if it he gave you.
That you are not able to understand that he didn't ask you a question is not my failure.

Anyhow I don't care to be the bitten dog here.
I've a hide like a rhino's

Junglemath
Posts: 54
Joined: Fri Sep 20, 2019 1:25 pm
Location: Minsk

### Re: Problem 713

hk wrote:
Wed Apr 29, 2020 12:51 pm
Actually Lilstalker didn't ask you a question.
Lilstalker translated the question of the problem to the translation if it he gave you.
That you are not able to understand that he didn't ask you a question is not my failure.
LilStalker wrote:
Tue Apr 28, 2020 8:00 am
What is the minimal number of tries that will guarantee that the device is working?
Is that not a question?

hk