## Problem 084

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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jaap
Posts: 559
Joined: Tue Mar 25, 2008 3:57 pm
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### Re: Problem 084

wancl wrote: Thu Oct 26, 2017 12:38 pmwhat is the difference between 'Go to next R (railway)' and 'Go to next R'?
There is no difference. They are two identical cards. The bit in brackets is just explanation of what R means.
wancl
Posts: 2
Joined: Sat Aug 06, 2016 1:50 pm

### Re: Problem 084

Ah, they're playing mind games!
Thanks for clearing that up
TexasRebel
Posts: 7
Joined: Sun Aug 02, 2015 8:14 pm

### Re: Problem 084

I'm having the same confusion so many others have had about doubles.

As the rules are, when the first and second double are rolled the player visits a square and performs any necessary action. I count this as a stop (and it is) before rolling the dice again.

some of the posts here seem to insinuate that there is the possibility of up to a (6+6) + (6+6) + (6+5) roll that wouldn't count the 12th or 24th space before landing on the 35th. Which is it?
HungryKoala
Posts: 2
Joined: Mon Apr 16, 2018 10:30 am

### Re: Problem 084

I believe this problem should be removed from ProjectEuler. Among my arguments: it is causing many people, including me, a lot of confusion. The problem is not correctly and completely formulated/stated, and it assumes some prior familiarity with playing this, or a similar kind of game. The cognitive difficulties and challenges I'm having into digesting what exactly is required, are immense. As this very forum discussion thread proves, the problem appears to be open to various different, contradicting with each other (inconsistent with each other) interpretations, which is not what mathematics and computer science, as exact sciences, are about. Moreover, depending on the background of people having played (or not) various variations of the game, the number of possible interpretations skyrockets.

Nowhere did I see any explicit wording about considering infinite number of turns, when calculating the probabilities. With the Closed Universe principle I would assume that whatever is not explicitly stated should be assumed to be false.

I think this kind of problem in not what PE is meant for. What I would expect in PE are clear, strict, formal definitions, that do not leave people wondering how to fill the gaps. Otherwise this would be more fit to take part in some literature/humanitarian science discussion.
v6ph1
Posts: 131
Joined: Mon Aug 25, 2014 7:14 pm

### Re: Problem 084

Why not?

A lot of problems here need a little pre-knowledge or understanding of the topic.
In any geometric problem, the term for parallel isn't explicit stated.
One of the most popular games shouldn't be a problem here.
All relevant rules are stated in the problem description.

There is no need to point out the "infinite" number of turns. This is clear after the read of the description and especially after reading the example string for 2 six sided dice.
HungryKoala
Posts: 2
Joined: Mon Apr 16, 2018 10:30 am

### Re: Problem 084

Well, that's just my personal opinion, but I believe that this problem has too many aspects which are open to interpretation. There is loose-to-none definition of what exactly the intended answer should be, and ill-defined and/or under-specified problems in general make little sense, as their lack of precise statement forces you to guess what exactly the problem author meant it to be. So instead of solving a real problem, I now have to first guess what version of the problem statement the authors envisioned in their heads, and only then embark on the real solution adventure.

As a bare minimum I believe that the problem wording needs a thorough rephrasing and rewriting, in order to eliminate all ambiguities that are still causing confusion among people.
tinnderbox
Posts: 3
Joined: Sun Nov 01, 2015 3:22 pm

### Re: Problem 084

Well, if you don't like the problem then don't solve it - nobody forces you to do so.
So far almost 10,000 people had the satisfaction of finding the correct solution, though.

Without wishing to provide a hint, I feel this problem is an excellent example of a certain concept.
On applying that concept the solution can be obtained in a rather elegant way, I felt.
Without recognizing that concept the problem probably becomes quite hard.

None of the problem wording looked ambiguous to me, by the way.
traxex
Posts: 66
Joined: Thu Oct 19, 2017 1:30 pm

### Re: Problem 084

To be fair, there are many different probabilities posted in the closed forum. Many solvers had different interpretations of some details and had to do some guesswork.

I remember very clearly that I could not reproduce the probabilities given in the problem and I did find the problem a bit frustrating. But I don't think it should be removed, it's part of ancient history now.
Technically, everyone is full of himself.
Jochen_P
Posts: 55
Joined: Mon Oct 05, 2009 10:47 am
Location: Stuttgart, Germany

### Re: Problem 084

Yay!

my code keeps insisting that "100024" is the modal string for two six-sided die
That's a tad bit frustrating ..

Ah, and I implemented the rule to just accumulate the doubles except there are 3 of them, otherwise my result would be "101918"

[edith says:] now that I ran it for a couple of times: it seems to produce the correct string on every 10th run or so [/edith shut up]
Last edited by Jochen_P on Tue Jan 29, 2019 7:11 pm, edited 1 time in total.
Jochen_P
Posts: 55
Joined: Mon Oct 05, 2009 10:47 am
Location: Stuttgart, Germany

### Re: Problem 084

Well, I sit here and are completely baffled.
Got desperate and tried my code with two 4-sided die, and guess what; Green Tick

 an admin may edit this if it reveals too much: had to revert to numpy for random dice throws as the standard random implementation in python is too unreliable for this small range, so now my results for the sample are consistent as well [/edit]
haroldgparker
Posts: 4
Joined: Sat Apr 24, 2021 1:19 am

### Problem 84

I have a question about Problem 84. The specification mentions that if you roll three doubles in a row, you must go to jail. As I understand it, in real-life Monopoly (the game), if you roll doubles, you also get to roll again. However, this latter detail is not mentioned in the specification. Which of the following patterns -- if any of them -- is correct for the problem?

Pattern1: A player starts on some square, rolls the dice (they're doubles), and moves to some new square where they end their turn. The same thing happens on their next move, ending on new square. On their third move, when they roll doubles yet again, they end that turn on the jail square.

Pattern2: A player starts on some square, rolls the dice, and gets doubles. As such, they don't move just yet, but roll the dice yet again, and after receiving doubles, they roll yet again. If they don't get doubles, they'll advance some large number of squares. If they do get doubles, they will end their single turn in jail.

I ask because, under Pattern1, the intermediate squares are part of the final probability distribution, whereas under Pattern2, they are not.
RobertStanforth
Posts: 1690
Joined: Mon Dec 30, 2013 11:25 pm

### Re: Problem 084

haroldgparker wrote: Sat Apr 24, 2021 1:30 am [...]
I ask because, under Pattern1, the intermediate squares are part of the final probability distribution, whereas under Pattern2, they are not.
I have merged this with the existing thread for Problem 084.

Pattern 1 is closer to the truth. On rolling a double that is not the third consecutive, they take that turn (which counts towards the distribution), and then proceed to another turn. This happens before play passes to the next player - although that last point is not important for this as there is only one player.
haroldgparker
Posts: 4
Joined: Sat Apr 24, 2021 1:19 am

### Re: Problem 084

Thanks! -- just solved it.