ASF Spoilers Thread

[cynic]

Initially there is a 2/3 chance of being wrong.

After the judge reveals one of the chosen boxes to be empty one is faced with a better chance of being right by changing over to the remaining box.

 

[keithj]

If you think the answer is that it doenst improve my chance of freedom by choosing the remaining box, then i struggle to see the point of the puzzle.

Could you explain it with 10 boxes ? You pick one, and then the judge reveals 8 of the others are empty. Will the odds change ?

 

[galumay]

Initially there is a 2/3 chance of being wrong.

After the judge reveals one of the chosen boxes to be empty one is faced with a better chance of being right by changing over to the remaining box.

I dont get your logic, i agree initially there is a 33% chance of your pick being right, but once the judge reveals the empty box there is now a 50% chance you have the right box, changing to the remaining one will mean you still have a 50% chance of being correct.

 

[galumay]

Could you explain it with 10 boxes ? You pick one, and then the judge reveals 8 of the others are empty. Will the odds change ?

The odds change of either of the remaining boxes being the path to freedom, but the odds dont change by swapping your choice from one to the other remaining box.

 

[cynic]

I dont get your logic, i agree initially there is a 33% chance of your pick being right, but once the judge reveals the empty box there is now a 50% chance you have the right box, changing to the remaining one will mean you still have a 50% chance of being correct.

No. If your first choice is wrong (2/3 likely) it will dictate the choice by the judge having to reveal the only remaining empty box indicating that there is a 2/3 chance that the unchosen box contains the pardon.

 

[cynic]

When the last two marbles are selected a coloured marble will be returned according to the rules. It will be the last remaining marble and it's colour will be known.

Edit: If all marbles are red at outset then last marble will be red, otherwise last marble will be blue.

 

[galumay]

No. If your first choice is wrong (2/3 likely) it will dictate the choice by the judge having to reveal the only remaining empty box indicating that there is a 2/3 chance that the unchosen box contains the pardon.

Huh? As i said, my first choice has a 33% chance of being correct, once the judge reveals one of the remaining two boxes to be empty, there is a 50% chance of either of the two remaining boxes containing the pardon.

Changing the box I have selected at this point will not change the odds from 50%.

 

[galumay]

When the last two marbles are selected a coloured marble will be returned according to the rules. It will be the last remaining marble and it's colour will be known.

Edit: If all marbles are red at outset then last marble will be red, otherwise last marble will be blue.

Its more complex than that, see my answer on the previous page. Reread the question too, he is asking if you can tell upon being told what number of balls are present - eg if their are 87 red balls and 46 blue, can you tell what the remaining ball will be? (it will be red)

 

[skyQuake]

I think you misunderstand what i said - and I cant understand what you are saying now!

The judge knows the contents of all the boxes.

He knows the box he opens doesnt contain the pardon. Given that we already knew that he knows the contents of all the boxes that implies that the other unopened box contains the pardon in this case.

It doesnt mean i cant pick the box with the pardon, just that i didnt this time.

If you think the answer is that it doenst improve my chance of freedom by choosing the remaining box, then i struggle to see the point of the puzzle. Obviously if the judges actions provide no new information then its 50/50 which box the pardon is in.

(maybe this one is just a really basic and simple puzzle and i am overthinking it??!!)

Wiki monty hall. They even made a US game show out of it!

Every time I have to work hard to understand it, then I get it. 6 months later I forget the reasoning again...

 

[skyQuake]

#7 make a snowball containing the $$ & throw it back over ?

Correct

#10. He's not wearing bowling shoes.... everyone else is.

Correct

#8 the alarm clock in the bookshelf

Correct

#11 elephant has a bandage on its trunk!

Thats no elephant! But close

#9 There's no outlet for the waste products after the hunny is sucked from the flowers ?


And a fun fact from wiki

Not quite but the wiki article is a huge clue

Answer to # 12 : Use the wrench to remove car tyre tubes and tie them to the bag of coins with the rope.

Correct!

 

[cynic]

Huh? As i said, my first choice has a 33% chance of being correct, once the judge reveals one of the remaining two boxes to be empty, there is a 50% chance of either of the two remaining boxes containing the pardon.

Changing the box I have selected at this point will not change the odds from 50%.

There is only a 1/3 chance of you being right by remaining with your first choice which means you have a 2/3 chance of being right by changing it to the remaining box!!!

 

[cynic]

Its more complex than that, see my answer on the previous page. Reread the question too, he is asking if you can tell upon being told what number of balls are present - eg if their are 87 red balls and 46 blue, can you tell what the remaining ball will be? (it will be red)

Okay I see your point.

If there is an uneven number of blue balls present then the result will end in a blue ball, otherwise it will be red.

 

[skc]

#7 - The river is frozen. Just walk across.

#8 - Cassandra Cat is hot! The libralian is clearly a geek. How hard can it be?

#9 - The company is listed on ASIC scam watch

#10 - No one wears a double breasted suit to bowl.

#11 - What animal is that in the middle? Ant eater?

#12 - Inflatable bags (inflated with the scuba regulator) are often carried by divers.

#13 - There's a pair of eyes hiding under the machine.

#14 - Are these cartoons from a left- or right-hand drive country?

#15 - The make/model/colour of the vehicle as supplied by one of the 6 eyewitnesses.

 

[keithj]

If there is an uneven number of blue balls present then the result will end in a blue ball, otherwise it will be red.

And the reasoning is...
There are 3 possible outcomes of a 'turn'
red,red -2R +1R nett result is one less red, but same number of blues
blue,blue -2B +1R nett result is one more red, but 2 fewer blues
red,blue -1R -1B +1B nett result is one less red, but same number of blues

So count of blues can only ever go down by 2 or 0, but reds can go up or down by exactly 1
Therefore blues that start with an odd number must end with an odd number (ie 1)

 

[bellenuit]

Okay I see your point.

If there is an uneven number of blue balls present then the result will end in a blue ball, otherwise it will be red.

I can't remember all answers given, but this is the correct one and some others may have got it too.

An even number of blues at the start means you end with just one red and an odd number of blues means you end with just one blue. You actually don't need to know the number of reds at the start.

The logic is as follows:

a. If 2 blue balls are picked, that will result in the box changing by -2 blue, + 1 red (2 blues are taken out, 1 red put back in)
b. If 2 red balls are picked, that will result in the box changing by -1 red (2 reds are taken out and 1 red put back in)
c. If 1 red and 1 blue are picked, that will result in the box changing by -1 red (1 red and 1 blue taken out and 1 blue put back in)

So no matter what is picked, the number of blue balls either doesn't change at all or changes by -2.

So if you start with an even number of blue balls, they will eventually be removed going 6, 4, 2, 0. When down to 2 blues, they will be either picked together and replaced by a red (a. above) so that all remaining balls are red and thus will result in -1 red each subsequent draw (b. above) until there is no blue and just 1 red or they will be picked individually with a red (c. above) but not depleted. If this keeps happening you will eventually have just the 2 blues, which will be removed and replaced by a red. So an even number of blues result in a red.

An odd number of blues will eventually go 7, 5, 3, 1. If that remaining 1 blue is on its own, that is the game end. If there are still reds and that 1 blue is picked with a red (c. above), then it keeps getting replaced so that there is still one blue, but reds are depleting by 1 each draw. Eventually you will just have 1 blue and 1 red, which when drawn results in a blue.

So an even number of blue, means you end in a red and an odd number means you end in a blue. You actually don't need to know the number of reds at the start.

 

[bellenuit]

And the reasoning is...
There are 3 possible outcomes of a 'turn'
red,red -2R +1R nett result is one less red, but same number of blues
blue,blue -2B +1R nett result is one more red, but 2 fewer blues
red,blue -1R -1B +1B nett result is one less red, but same number of blues

So count of blues can only ever go down by 2 or 0, but reds can go up or down by exactly 1
Therefore blues that start with an odd number must end with an odd number (ie 1)

Sorry, keithj, I didn't see your explanation until I had made mine.

 

[bellenuit]

You are a criminal found guilty of a serious crime and have been sentenced to death. The judge, being a puzzle freak, decides to give you a chance of avoiding death.

He shows you three closed boxes on a table. You are told two are empty, but the third contains a royal pardon. You are to point to one of the boxes and if it is the one with the pardon inside you will be freed, otherwise you will be put to death.

You point to one of the boxes. The judge, knowing which box contains the pardon, opens the lid of one of the remaining boxes, one which he knows for sure doesn't have the pardon and shows you that it is empty.

He then tells you that he will allow you to change your mind if you want. You can either stick with the box you originally pointed to or you can pick the other unopened one instead. Assuming you do not want to die, does changing you choice increase your chance of freedom or make no difference. Explain why.

Yes as someone pointed out this is the famous Monty Hall problem that caused a lot of disputes between mathematicians since it was first postulated. Only the diehards do not consent that you increase your odds by switching to the other box.

The logic is quite simple and I can't really see why it would be disputable. Your chances of being right in the first pick is 1/3 and your chances of being wrong 2/3. Because the judge pointed out which of the other two didn't have a pardon, your original choice still remains at 1/3, but the unopened box now gets the combined probability that was previously attached to the other 2, namely 2/3. So your chances of being pardoned increases if you switch.

As someone pointed out, think if there were 100 boxes with only 1 pardon. You pick one and the judge opens 98 of the remaining 99, all of which he knows are empty. To assume your probability of not switching jumps from 1/100 to 1/2 is absurd. The other unopened box now carries the probability that the combined 99 previously carried, namely 99/100, so switching is the thing to do.

 

[galumay]

Y
As someone pointed out, think if there were 100 boxes with only 1 pardon. You pick one and the judge opens 98 of the remaining 99, all of which he knows are empty. To assume your probability of not switching jumps from 1/100 to 1/2 is absurd. The other unopened box now carries the probability that the combined 99 previously carried, namely 99/100, so switching is the thing to do.

Your whole explanation makes no sense to me! Not saying its wrong, just that I still dont get it!!

If i have picked 1 box out of 100 i have a 1% chance of being correct, if the judge opens 98 of the 99 left and proves they all have nothing in them, we now have 2 boxes, 1 with the pardon, 1 without. Its patently obvious that which ever box you choose has a 50% chance of containing the pardon, so switching cant change your odds.

Your reasoning makes not the slightest sense to my dumb head!!

OK, read the wiki and all i can say is i am happy to be wrong along with so many geniuses and mathematicians! Still dont believe it though.

 

[skyQuake]

Your whole explanation makes no sense to me! Not saying its wrong, just that I still dont get it!!

If i have picked 1 box out of 100 i have a 1% chance of being correct, if the judge opens 98 of the 99 left and proves they all have nothing in them, we now have 2 boxes, 1 with the pardon, 1 without. Its patently obvious that which ever box you choose has a 50% chance of containing the pardon, so switching cant change your odds.

Your reasoning makes not the slightest sense to my dumb head!!

OK, read the wiki and all i can say is i am happy to be wrong along with so many geniuses and mathematicians! Still dont believe it though.

Here's a simple explanation:
Imagine now instead that instead of revealing a box,
The judge lets you
a) keep your initial choice
b) open BOTH remaining boxes.

b) is now a no brainer (switching) 66% vs 33%

b) is also the same as giving you both boxes (with one already open)

 

[skyQuake]

Correct:
7 - Throw money across in a snowball, walking on thin ice is too dangerous
8 - Alarm clock on shelf
10 - He's not wearing bowling shoes.... everyone else is.
11 - Anteater has no teeth!
12 - Use the wrench to remove car tyre tubes and tie them to the bag of coins with the rope.

Unanswered:
9. Wiki gives clue
13. Again a general (actually fairly specific) knowledge q
14. Left/Right hand drive not actually relevant
15. Look for visual clues