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An Impossible Bet

An Impossible Bet


This has nothing to do with physics, but I
want to make a bet with you and 99 other people: 100 in total. You’ll all stand in a line,
take a one dollar bill out of your pocket and write your position in line on the bill.
Then I’ll collect the bills, take them to a separate room, put each one into its own
one of 100 identical boxes, and randomly rearrange the boxes. The game is this: each of you come into the
room and try to find which box your bill is in – but you’re only allowed to come in one
at a time, you’re only allowed to peek in half of the boxes, and you aren’t allowed
to change anything about the boxes or move bills around. If you find your own bill, great!
Show me that you’ve succeeded and then leave the bill in its box. And regardless of whether
or not you find your bill, you have to leave the room by a different route so you can’t
tell anyone else what you’ve seen, and the room is then reset before the next person
comes in. At the end, if all 100 of you have successfully
found your own bills, you all win and I’ll give each of you a hundred dollars plus the
one you started with! But if any one of you doesn’t find your bill… I keep all the dollars.
You are allowed to plan a strategy together with the other players before any of you come
into the room, but no communication afterwards. The question is this: should you take the
bet? To recap, every person gets to look in half
of the boxes, there’s no communication between players after they go into the room, and you
only win if every single person finds their own bill. $101 dollar payout if you win, nothing
if you lose. Take a moment to think about it, then click
the links on screen or in the description to make your choice – and find out what the
correct answer is.

100 comments on “An Impossible Bet

  1. The strategy is this,and I have seen a similar riddle by TED. So the first person open's their respective box hence the 1st box. If he/she finds their bill, then go on, but most likely not. If not, they go to the box with the same number as the bill you get. Ex: the first box contains a bill marked 51,then you go to the 51st box and repeat the process until you find your bill. I'm too lazy to count the pobablility, but it's the best method to find your money.

  2. My strategy would be..

    Bring a glue bottle with you. Person 1 looks through 50 boxes, and if there isn’t anything in it, glue it. Next person can’t open them if there glued, so they glue the other half, and person three only opens the ones that aren’t glued.

  3. The bet is only logical if the odds of winning are better than 0.990099%.

    The odds for the first person to win are .5^1. The odds of each subsequent player also choosing their box is .5^(their number in line).

    That means the odds of each getting the correct box is .5^100. Which is equal to 7.88×10^-31 which is far worse than 0.990099%.

  4. Yes. One strategy is if you open box 61 which has a 2 dollar bill in it, then next open box number 2 and proceed like this

  5. No don’t take it if you think about it each Person 100 in total has a 1/2 to find there bill so 1/2 x 1/2 is already a 25% of winning and that shrinks every time drastically and you do it 100 time so no

  6. hmm I heard this the strategy to minimize the same boxes being open by different person increasing the chance of each person initial chance of 50/100.
    each person must first go to the number of their assign bill then if the bill is not them they will go to the box with the picked bill assigned, so on and forth until they get their bill

  7. If they are the ones placing the bills in boxes, can’t they just all agree to put them in numerical order so everyone knows where theirs is?

  8. Write down on the floor the contents of the 50 boxes. Then th 2nd writes the other 50 and then u have a 50% chance of winning

  9. I seen something similar to this on another video but it was with musicians and their instruments in a box, in it what they did was they opened their box and whatever instrument was in it, they then went over to that box and so on. So for this puzzle they’d say if you are number 1, open the first box, if it says 77 on it, go to box 77 and so on, I can’t remember why it works but it’s something about cycles

  10. Sure I would take the best because if I lose I only lose 1 dollar. Is not like a casino were you lose all your life savings on gambling.

  11. What if everybody takes whatever bill they see first and not necessarily their own? Insta win, since who would record everybody's number on their dollar.

  12. go to 50 box..
    take the bill out…
    and leave with 50$..
    that's 50$ payout..
    or bribe minutephysics 50$ and leave with 50$..
    simple

  13. Open the box of ur number (so person 16 will open box 16 in the line) and if that's ur bill ur done! If not open the box of that bill on it (so if box 16 has bill 28 in it u open box 28) keep on going till u find ur bill cause this has a fairly high chance of success. And yes because if u loose u loose $1 or €1 or £1 whatever it currency is but of u win u get 100 of whatever ur currency is.

  14. you first chose any random box then if it has yoir bill GOOD LUCK but if no and you went to box 7 and the bill says 90 go to the 90 box and keep on going

  15. I would take the bet. Go into the room. Open ALL the boxes and take out EVERYONES Dollars, walk out, tell the guy you couldn't find your dollar and walk away with the jackpot in your pockets.

  16. Assuming the boxes are labeled, first go to your number box and then go to the box which corresponds to the one you found in yours. Do that for each bill you find until you find yours.

  17. Take the bet!! When you open a box proceed the the box with the corresponding bill number and continue this pattern until you find your bill

  18. Dont take it because even if you win since you must put in your own dollar if you win you just get your own doolar back

  19. who wouldn’t take the bet? if you lose, then you lose $1 not a big deal. but if you win you get $100 more than you started with.

  20. 1) pick the that is of the same number as your bill (eg you number is 48 you go to the 48th box)
    2) if it is your bill, congrats. If it is not go to the box that is of the same number as the note you saw (eg. You see 56 you go to the 56th box)
    3) every player does this, the chances of success are around 35%

  21. I would take the bet and what I would do is look in one box then go to a number box with the bill until I did the 50 turns or found my bill

  22. Basically… you need to maintain a closed loop. i.e rather than random searching of the boxes the system should be that you start with your number. So if I’m 17, I look in box 17 and if I find bill number 66, I then look in box 66 etc. So the chance that the loops will be 50 or less is about 30% and tbh you’re only losing a dollar so yes.

  23. Chose the number on your bill. Then chose the number that was in the box. For example if you had bill #1 chose box one, and in box one there’s bill number 3 chose 3

  24. The people line up outside the room from with their numbers 1 to 100 in order. The first guy will search all of the boxes on the left side of the room. (Note that this has a 50% chance of sucess because it is over if the first guy does not find his own bill) (The following is a stretch, because you are communicating with the people in the line, even though you are not going back to the group in the beginning. I'm a rebel) The first person will then yell out "left," or "right," (depending on which side they chose) and then yell every number on that side. Hopefully the first person also finds his own on that side, which is bill number 1. If number 2 heard "2" yelled by the first person, they will go to the same side the first person went, (note that the first person also calls out which side they went, left or right) and go through all of those boxes until they find their own. If the second person does not hear "2" yelled by the first person, they will instead go the opposite direction. People 3-100 will do the same thing that person 2 did. Note that 2-100 will need to remember if person 1 called their number or not, but if $101 is on the line they should remember.

  25. U open first box and for example if on the bill there is number 32 u go to 32nd box and u find bill with number 71 and u go open that box and so on there is more than 68% that u are going to make it

  26. 1/2^n … when (n) = 100 then you get 1/2^100 …. however for just $1 ? I think you should totally take the bet lol

  27. Solution: go get a random box. Look the bill number nad go to the box corresponding that number. Repeat as long as it takes to find your bill.

  28. Solution I think

    The first person goes in the room and check the box that has his number (for example his number is 38 he will go to box 38 and check in the box).if the number is 47 he will go to box nuber 47 and check in that box.he will do repeat this until he finds his number.
    The next person who goes in will do the exact same but start with his/her number.

    Tell me if I'm right or am I to late

  29. I’d take it. Go to the box with your og number in it. After, go to the box with the number that has the number of the bill you just grapped on it. No idea how this works, saw it on a Ted Riddle video once.

  30. when they write the number on the 1 dollar bill they can write 2 numbers on either side so on one side there would be the number 1 and the other side number 2. so if they can only view 50 boxes it would be sure that they would find their number.

  31. Solution: Open the box with your number than whatever number bill it is go to that number box and so on until you find your bill
    This has a 35% chance of working and getting $101 (unless they completely ignore you)

  32. Take the bet:
    1. First person to go in chooses his number(Example:6) box.
    2. So he goes to box number 6. If the number inside is 64, he shall proceed to box 64.
    3. Repeat the process until the box is found.

  33. You should take the bet an use this strategy:
    Every person that enters the room choose the box that matchs with the number that you wrote on your dolar at the beginig. If your dolar is not there you look at the number on the dolar and continue to look on the box that matchs with the number of the last dolar you just saw. If you conitinue and follow this process and every single person follows this strategy you all have maybe a 30 percent chance of winning. It is a very good deal knowing you have a 10100% profit for a 30% chance of wining

  34. Answer (l am actually serious)
    Yes take the bet.
    For example: You had the 64th bill
    1. Go to the 64th box
    2. (Assume its the 21st bill in the box) Go to the 21st box
    3. Repeat the same process, you will get your bill.

  35. IT IS SOLVEABLE.
    Say you had the 45 box, go to there and see what number is there. If it’s 74 go to the 74th box. Repeat = PROFIT.

  36. 0.5/100 = 0.005% = a 1 in 200 chance of winning a 101 fold increase on your money so you should not take the bet because in the long run, it isn't feasible you would play 200 times spending £200 and winning £101

  37. So here’s a thing that does somewhere around 30 percent of winning

    So look in the first box, the number of the dollar bill in there will be your next box and so on

  38. Should I bet $1 for the almost impossible chance of winning 1 cent? Yeah, I think I'll pass up on that wonderful opportunity…..

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