Hi Barry, I've just sent you two solutions reaching the same result by very different methods. I'll drop onlookers a subtle hint about the general solution. Dr Evil will be carrying a very heavy bag.
Hi Barry, I've just sent you two solutions reaching the same result by very different methods. I'll drop onlookers a subtle hint about the general solution. Dr Evil will be carrying a very heavy bag.
Two prospective solution received so far. Still time for other interested parties to try out their problem solving skills.
Deadline 24:00 Wednesday, 14-Jan (GMT+11)
So einfach wie möglich, aber nicht einfacher - Albert Einstein
Make that three solvers so far. Don't delay for a chance to get in "on the ground floor" for the fad that is sweeping the online BB community.
That didn't come across to self-obsessed or needy, did it?
So einfach wie möglich, aber nicht einfacher - Albert Einstein
OK, Only 30 hours to the deadline. I have solution from MS and KB. I also have a solution from DR but he has subsequently sent me an PM that he would like to revise it. So unless I hear back I will assume the previous submission is withdrawn - leaving me with two solvers.
I have also had the opportunity to prepare my solution as clear and correct as I can make it. Hopefully, it is of some use. Due to the symbology required I've published this as a PDF file and will be linking to it from my solution post.
I'm also thinking of quoting the solvers' PMs directly in the solution post. I trust this is not a breach of protocol as I don't believe the solvers would have assumed confidentially in their messages, and would assume their PM would be posted anyhow.
If anyone doesn't want me to do this, please let me know. I know Matt is away and I'll have to deal with his ire (if any) on his return. However, Matt's submission is very interesting and I really want to include it the solution post.
So einfach wie möglich, aber nicht einfacher - Albert Einstein
I certainly assumed this - it's not explicit from your previous posts but strongly suggested. Anyway Matt doesn't believe a PM is confidential anyway (past experience) so his consent may safely be taken for granted.Originally Posted by Barry Cox
That's ... disturbing.However, Matt's submission is very interesting and I really want to include it the solution post.
I am worried that he may have got it right. :shock:
I've just sent my solution BJC
Itwas clear from your post that this was the case. It is less so from Matt's message.Originally Posted by Kevin Bonham
I won't say too much more prior to the deadline as I don't want to confer any information about the possible solution. But I stand by my original posting, Matt's solution in indeed noteworthy.Originally Posted by Kevin Bonham
22:30 to go!
So einfach wie möglich, aber nicht einfacher - Albert Einstein
Yep, message received. Three solvers registered so far. But it is not too late for someone elseto have a crack at it.Originally Posted by David_Richards
So einfach wie möglich, aber nicht einfacher - Albert Einstein
Why not have a go? 7:30 to go - it's not too late.Originally Posted by arosar
So einfach wie möglich, aber nicht einfacher - Albert Einstein
OK. It is the hour of reckoning. For my worked solution look at the following link. If you have any questions let me know here or by PM, whatever is your preference.
Worked Solution
The final scores were
Matt: 6/8
Kevin: 7/8
David: 6/8
Interestingly each person came up with a new approach on the problem all of which were basically correct. However, Matt and David went astray, I think by applying too much intuition. Perhaps, that's unfair in David's case as it may have just been a clerical error.
Also it was noted that it was the exclusion of the 20/0 distribution which caused the probability to not be 0.5 This is a very interesting result and probably answers Matt's original question way back when.
The other interesting result is that when distributing an even number of things between two possibilities (say 20) the 12-8 distribution is more likely than the 10-10 distribution. This would come as no surprise to Bridge players but is an interesting general rule. With an odd-number (say 19) then 10-9 is more likely than any other single possible distribution.
Anyway, pretty good results all round. I'll now post each submission in separate emails with some short comments.
Remember, judges decisions are final yada yada yada, except as I said above I am willing to enter into correspondence.
If anyone is interested I can come up with some other maths problems, not necessarily related to probability. If you're interested let me know.
So einfach wie möglich, aber nicht einfacher - Albert Einstein
It sort of does make sense. In fact I was quite surprised as to the simplicity and insightfulness of this line of reasoning.Originally Posted by Matthew Sweeney
Unfortunately, Matt forgot one thing (the fact that removing the 2 possible distributions changed the basis of all the probabilities
from 2^-20 to 1/(2^20 - 2), but that it all.
However, this is the problem of relying too much on intuition. It can lead you to an original solution but the lack of rigour can cause you to make mistakes too. Better to hve the inspiration and then the technique to prove the insight correct.
Regarding the scoring.
(a) 2 points
(b) 4 points - the insightfulness was remarkable. Unfortunately, the final answer was slightly off and there was a calculation error in the decimal side.
1/1048576 is approximately 0.00000095 so the answer should have been 0.49999905
Total Score: 6/8
So einfach wie möglich, aber nicht einfacher - Albert Einstein
Almost full marks! I like the long way as this was basically my starting point too. The short version is good too. Unfortunately with this solution there was again an error with decimal side of the calculation (probably just a transcription error).Originally Posted by Kevin Bonham
262143/524287 is approximately 0.49999905 (8 dpl)
I assume you got carried away with the 9's and included one too many. Anyway, just subtracting a point for that the score is...
(a) 2 points
(b) 5 points
Total score: 7/8 - and our winner of round 3.
So einfach wie möglich, aber nicht einfacher - Albert Einstein
Originally Posted by David_Richards
A valiant effort working from second principles but not quite right. Your table is almost complete I would have added the following line
0/19, 1, 0
Which would have accounted for the all black possibility and lead to the result 262143/524287.
However, everything else (including your calculation of the answer to 8 decimal places) was accurate so I'm scoring your answer on a par with Matt's - on the right track but not quite right. Possibly, lack of rigour in some of the reasoning leading you astray - possibly just an oversight. Score...
(a) 2 points
(b) 4 points
Result 6/8
So einfach wie möglich, aber nicht einfacher - Albert Einstein
Originally Posted by Barry Cox
I was using a calculator which couldn't hold all the decimal places, so I had to subtract the .499999 off to get the rest, and must have simply written one two many 9s down then not checked it. Dumb.
Careless errors like that were always my weakness but at least I had the method(s) right. :?
Feel free to post more, except I'm allergic to trig, geometry and calculus.
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