Monty Hall puzzle 4

[assets]

I am looking for the Monty Hall puzzle I saw it about two week ago but could not find it last week. It has a puzzle in it about bases. Can someone give me the link to the Thread please.

Never give up never give in.

There are no short cuts to anything worth doing

 

[kwbMitel]

It wasn't here, I can assure you.

A "Monty Hall" puzzle has to do with having 3 choices and being given the option to change your choice after a wrong door is revealed. Exactly like the Game Show - Let's Make a Deal which had the host Monty Hall.

I can't imagine a relationship to bases.

The Monty Hall scenario is quite storied in that most (in my experience) people cannot/will not accept the probability of winning increasing (doubling) if you change your choice after the reveal.

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What's most important is that you realise ... There is no spoon.

 

[strongm]

> most (in my experience) people cannot/will not accept

Indeed, many highly-respected and highly-qualified mathematicians refused to accept the correct answer when the problem was publicised by Marilyn vos Savant back in erm ... (fx: google) ... 1990

 

[ChrisHirst]

thread1551-1735489

Chris.

Indifference will be the downfall of mankind, but who cares?
Time flies like an arrow, however, fruit flies like a banana.
Webmaster Forum

 

[kwbMitel]

@ strongm

I've been having some success convincing people with the following description.

Delay the door reveal
Offer the contestant the option to either stick with their first choice or have the best prize from the other 2 doors
Now it is obvious that 2 doors are better then 1 when the choice needs to be made
The reveal of the dud door is meaningless in this context and is more easily demonstrated to be meaningless regardless of when it is revealed.

**********************************************
What's most important is that you realise ... There is no spoon.

 

[strongm]

Intriguing. I need to have a think to see if that represents the same problem, though.

 

[assets]

Thank all no Chris its not the tread I was talking about. Yes to all I know the answer about the three doors. But the original post also had a puzzle where the answer was based on bases the next number in the series was 1111 but the one before was 50 cujancenturan pointed out it should have been 120. I hope this explains a bit better.

Never give up never give in.

There are no short cuts to anything worth doing

 

[kwbMitel]

@assets

I thought you meant recently!!!

That was one of my posts actually and I done goofed when I recreated it from memory.

It was in the Squaring the circle forum - thread1229-1601460

The part you are refering to is posted on 26 Apr 10 14:10

What is the next number in this sequence
15, 16, 17, 21, 23, 30, 33, 50, ???

The actual sequence should be:

15, 16, 17, 21, 23, 30, 33, [highlight #FCE94F]120[/highlight], ???

**********************************************
What's most important is that you realise ... There is no spoon.

 

[kwbMitel]

@ Strongm re:>> I need to have a think to see if that represents the same problem, though.

It does not matter whether the dud door is revealed or not before the choice if you are offered the best choice of the 2 remaining 2 doors

In the classic game where the reveal is before the choice you are actually being offered the best of both but natually you wont take the one known to be a dud.

There is a 1/3 chance that both are duds but you play the odds, you take your chances, it's still best to switch.

**********************************************
What's most important is that you realise ... There is no spoon.

 

[strongm]

>thread1229-1601460: Interesting Probability Puzzle

Ah, that was a fun thread.

 

[strongm]

>It does not matter whether the dud door is revealed or not before the choice

Oh, not disagreeing at all. Just needed to make sure I could see it was the exact same problem. And it is!

 

[ChrisHirst]

where the answer was based on bases the next number in the series was 1111

So number "base" not actual 'bases' then,

Chris.

Indifference will be the downfall of mankind, but who cares?
Time flies like an arrow, however, fruit flies like a banana.
Webmaster Forum

 

[assets]

THANKS everyone you ALL have been of a great help so hope the stars show up if not will have to try again to give you one. The Marilyn vos Savant has some good links people will still argue about the result. But that good to get people involved. As William S said To switch or not the Switch that is the question.

Never give up never give in.

There are no short cuts to anything worth doing

 

[assets]

For those who are reading and have not posted. I explain what we are talking about:

15 in base 10 gives 15 (15)
15 in base 9 gives 16 (9+6)
15 in base 8 gives 17 (8+7)
15 in base 7 gives 21 (14+1)
15 in base 6 gives 23 (12+3)
15 in base 5 gives 30 (15+0)
15 in base 4 gives 33 (12+3)
15 in base 3 gives 120 (9+6)
15 in base 2 gives 1111 (8+4+2+1)

Again thanks for all who helped


Never give up never give in.

There are no short cuts to anything worth doing

 

[Olaf Doschke]

This sequence of 15 in different bases is nice. You can also reverse the sequence, then you'd get

1111, 120, 33, 30, 23, 21, 17, 16, 15, 14, 13, 12, 11, 10, F, F, F, F, ....

It would be too obvious. 1111 is a strong hint and F of course is disclosing, that it's not all base 10 numbers.

But even only revealing from 120 to 10, the part of the sequence just decrementing would give a hint.

And finally, if you only reveal the part from 17 to 10, Occam's razor would suggest the sequence is simply a countdown.

Bye, Olaf.

 

[kwbMitel]

@Olaf (or anyone else for that matter)

When I first encountered this puzzle, I had to look up the answer

I thought it was interesting enough to remember it but I disagreed strongly with the full answer.

The final number offered in the sequence as part of the answer was: 111111111111111

Personally I have several arguments as to why 15 one's is not continuation of the previous numbers but I'm curious if you would accept that number.

**********************************************
What's most important is that you realise ... There is no spoon.

 

[Olaf Doschke]

I wouldn't have seen the pattern of 15 in different bases myself, too, if assets wouldn't have explained it, so don't worry about that, it's really hard to think out of the box of decimal numbers, if it's not obvious enough from the context.

In regard to 111111111111111:

http://en.wikipedia.org/wiki/Unary_numeral_system

The unary system is fitting in one aspect - it only has one digit, no matter if it's 1 or |. But it differs in not being a positional system and for that matter doesn't fit into the sequence. If you'd want to retrofit the unary system into a positional system, where a position of a digit in a number has a weight or base value you multiply with a digit, you'd need to define the weight of each position as 1^position and since 1^N is 1 no matter what N is, even for N=0, all positions would have the same weight of 1. So far so good. But as said already all normal positional systems have a factor for each position, the digit, going from 0 to N-1. For base 1 this would mean the one digit wouldn't be 1 but 0. But 0 as a factor would mean you could only represent the number 0 and so the unary numeral system doesn't fit into the sequence of positional numeral systems. We all know a but more complex extensions of the unary numeral systems by the roman numbers, having several abbreviations for larger numbers, that of course are not handy with just one digit. If you accept there is no 0 in the system it retrofits in that aspect, too, but I am with you the sequence ends (or starts) with 1111 in base 2.

Bye, Olaf.

 

[assets]

Roman numerals on a clock 4 is IIII and not IV ( for 15 you have 15 I big number), so as if you were counting animal and cutting a notch in a piece timber. you would have IIIIIIIIIIIIIII notches if you had 15 animals. So I agree with answer

Never give up never give in.

There are no short cuts to anything worth doing

 

[kwbMitel]

@Olaf - you nailed 2 of my reasons for not accepting 111111111111111 as a base 1 representation of 15

The strongest argument in my mind this one:

all normal positional systems have a factor for each position, the digit, going from 0 to N-1. For base 1 this would mean the one digit wouldn't be 1 but 0. But 0 as a factor would mean you could only represent the number 0 and so the unary numeral system doesn't fit into the sequence of positional numeral systems.

I would have said it differently but I like your way better.

**********************************************
What's most important is that you realise ... There is no spoon.

 

[assets]

Yes it not base 1 that why I used I and not 1. Odd or Evens numbers. Number go odd, even, odd, even. So you may say 0 (zero) is even it fall between two odds. BUT it doe not meet the test an even number can be divided by 2 so ) is not even. So in my example if there is no cuts on the timber then it 0 ( we do not know if 0 or just a bit if timber). But 0 can not be in base 1 as it does not exist. Just a counting system like for 5 you have IIII with the fifth I at an angle to make counting easier.

Never give up never give in.

There are no short cuts to anything worth doing