British Lung Foundation
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This puzzle may ring a bell with some of you. If so, please refrain from jumping in too soon:

Someone shows me 3 closed boxes and tells me that 2 of them are empty and one contains loadsa money.

He tells me I can pick one box and win its contents, if any, so I pick a box.

Then he, who knows which box the money is in, opens one that I haven't picked, shows me it's empty, and asks me if I'd like to switch my choice to the other unopened box.

Just to be clear, he has no hidden agenda in giving me this option, it's not his money, he's not my friend, he doesn't care whether I win it or not.

Should I switch?

32 Replies

it doesn't matter coz there are 2 unopened boxes - the one you picked and the one he didn't open! x

I agree-- 50/50 odds either way. Don't make a difference. I would almost bet money, you should switch. Answer can't be that easy. Not with our Stilltruckin!

😆😊 xx

if 2 are empty and one is shown to be empty if it is not an empty box that has been lifted it would be heavier. It would also show he was fit for work according to ATOS

cx

yes my thinking is you should switch. It is more likely that the one left is not empty, compared to the one you have picked (based on the initial likelihood with 3 boxes where it is less likely that both left behind boxes are empty than the one you picked is empty).

Well done jenss. xxxx

Thanks Sassy Have a great Easter with the family!

You too. xxx

"He tells me I can pick one box and win its contents, if any, so I pick a box."

When you picked the box you won nothing, so do the switch.

Are you a lawyer? That's a clever answer but would make it a trick question. There are no tricks, if I switch then the one I switch to is the one I pick.

I didn't continue on the lawyer thing from my patrilineal side.

I would stick to my first plan as I have not opened it yet.

Yes - switch. Jenss theory makes sense - I think. I can never work these out. Jan

don't swap

Switch,this was done on tv years ago ,I am sure maths teachers phoned up and said they were wrong.You chose your box with a choice of 3 so your box has a 1 in 3 of having the money.There were 2 boxes left when 1 was opened so the 1 left has a 1 in 2 chance of having the money.

I would not switch on the theory that he knows which box the money is in, so if I had picked the box without the money in it he would not offer me a switch..

Please note that I added the following clause this time:

"Just to be clear, he has no hidden agenda in giving me this option, it's not his money, he's not my friend, he doesn't care whether I win it or not."

It's not a trick question. One choice or the other definitely gives a better chance of winning.

no I would not swap - why would he open a box and show me it is empty - if I have chosen an empty box he would surely open the box of money to show me it did exist -and that would be it my choice would have been made but he does not do this - why - because I have chosen the one with the money - so yes I should keep the box as it has the money in - well that is just my reasoning - it maybe I'm being too devious ha, ha, come on stilltruckin put us out of our misery - good puzzle whatever the answer - thank you xx

See my reply to Sohara above, there's no psychology involved.

I'll give the correct answer a bit later, once it seems there will be no more responses . . .

Undine has made the most reasoned response and I agree with them.D. 👀

ok my guess is that it will be worked out on some probability theory but I still like my answer ha,ha xx

Jens sussed it.

Clearly the box I first picked has a 1/3 probability of containing the money.

Therefore there is a 2/3 possibility that the money is in one of the other two boxes.

Once one of those two boxes is known to be empty, then the other one has the 2/3 probability all to itself.

Therefore by switching the probability of winning increases from 1/3 to 2/3.

I think what Stewart 58 says is the correct answer. After the initial choice and revelation, whatever you do, whichever you choose, you have a 2 to 1 chance of getting the money.

Actually that not exactly what he said. But if you don't 'get' my explanation above, then look at the practical outcomes:

Label the boxes A B C. Say the money is in A.

Then, if you pick a box and stick with it there are 3 possible outcomes:

Pick A Win.

pick B Lose.

pick C Lose.

And if you pick a box and switch after being shown an empty one there are 3 possible outcomes:

Pick A, switch to either B or C, Lose.

Pick B, see C is empty, switch to A, Win.

Pick C, see B is empty, switch to A, Win.

Now say the money is in B and do it all again - same result.

Say the money is in C and do it all again - same result.

Yes very clever but there is a fundamental flaw in this as I see it, if I initially choose the correct box with the money in my being clever and using the above reasoning will cause me to lose the money so all the odds in my favour for making the switch are useless. I do realize that initially I am more likely to chose the wrong one having a choice of 3, and of course see that it works if I chose an empty box but that does not necessarily mean I will - so tis all a question of luck or chance in the end. But thank you it got me thinking. xx

Yes, luck comes into it, but it's not entirely random. it's a matter of probabilities. If you initially pick the money box and then switch you will lose, but it's twice as likely that you will initially pick an empty box and by switching will win.

yep undine and you see - I picked the right box in the first place so now I am off shopping

mmmmmm you had nuffink to start with so you not lose in 1s place what ever box it is in

A most perspicacious observation

In any series of plays sticking enables you to win 1/3 of the time and switching 2/3 of the time, conditional, as you say, on an empty box being revealed. Being given the option to switch after that is the equivalent of being offered 2 boxes for the price of one . . .

The only way the odds would be 50/50 is if you alternated sticking and switching, so that in a series of, say, 24 plays you win 4 out of 12 of them by sticking and 8 of the other 12 by switching, thus winning 12 out of 24 . . .

stilltruckin, NO1 It reminds me of tommy cooper and his "disappearing egg". he pressed on the egg (which was on a lever with another egg) and it appeared on the other side of the table through a hole, as Tommy laughed his head off. hahahaha! Mic