That’s a brutal April Fool’s joke. Dave, you bastard!
I don’t care what I saw on Mythbusters. That plane is not taking off.
Siren
1584
I just received a logic puzzle as a part of my interview process for a position as an Executive Assistant. Gotta love the startup culture!
I present it to you all here, especially considering I apparently did not answer it correctly.
You are the oldest of five contestants on a game show. You are given fifty $100 bills to divide between you and the other contestants. Because you are the oldest contestant you get to propose how the $100 bills should be divided. The other contestants will vote on your proposal. You want to make a proposal that will yield you as much money as possible. The other contestants are all very smart, very rational, and they will vote so they get as much money as they can given the rules of the game.
When you make your proposal, if at least half of the contestants (including you) agree to your proposal, then the $100 bills will be divided according to your proposal. But if fewer then half of the contestants (including you) vote for your proposal, then you will be removed from the game (in which case you can’t vote anymore and you don’t get any money) and then the remaining contestants will continue on with the next oldest contestant getting a chance to make a proposal under the same set of rules. This process continues until a proposal succeeds.
What would be your proposed division of the $100 bills and why?
I don’t understand why we need to know how the process continues. [If when you’re removed you can’t vote any more and you get no money, then who cares what happens after you are removed? - strike this question from the record! see my next post] Also, why would you ever vote against your own proposal?
These might be part of the riddle for all I know, but I sort of doubt it. Do you know?
Oh… I bet we see how the process continues because of this:
they will vote so they get as much money as they can given the rules of the game
It’s part of the riddle because the younger guys have a reason to vote against you, because each person who gets voted ‘no’ to increases their expected payout.
The real answer is “I write a Python script to answer the question”.
It doesn’t matter that the younger guys should vote against you because all the literature suggests that people use about three different mutually exclusive methods for analyzing this king of thing.
I’m sure a game theoretician could write a 200 page dissertation on this, but the fact is that if somebody really presented five people with this situation the result would almost certainly have nothing to do with games theory.
Unless you put them on an island and let them scheme about it for three months. And reality TV has proven that you need to offer a million dollars to get people to suffer through that.
Long story short, these interview questions are bullshit and the only thing they do is create an echo chamber of back-slapping for the interviewers to feel good about themselves when they pick the candidate that comes up with the reasoning that they already decided was the “right” reasoning.
Ooo, ooo, no, I think I got it!
I split the money 48/1/0/1/0, where I’m in position 1 as Player 1, second-oldest player is in position 2 as Player 2, etc. I claim that Players 2 and 4 must accept any amount of money tossed their way, so they’ll vote YES for this split.
Player 4 cannot allow the vote to proceed until she is the one making the proposed split, because Player 5 will vote NO to any proposal she makes, and then claim all of the money himself. So Player 4 will vote YES on any vote that gives her even one bill.
Player 3 knows this, so if the vote gets to him, he will propose 49/1/0. Both he and Player 4 will vote YES to this proposal.
But Player 2 knows this, and since Player 3 will get 49 of the bills if the vote gets to him, then Player 2 cannot let the vote get to her; after all, Players 3 and 5 will surely vote NO to any proposal Player 2 makes. So Player 2 will accept even one bill, just like Player 4.
=============
After typing this up and re-reading it and thinking about it a little more, I’m concerned with the statement I bolded. I think Player 5 cannot afford to let Player 3 make the 49/1/0 proposal, so cannot allow Player 3 to make a proposal. So Player 2 could make a proposal like 48/0/1/1, and would receive supporting votes from Players 4 and 5. Hmm…
Ezdaar
1590
Perhaps I misunderstand the rules, but if the remaining players are 4 and 5 then any proposal 4 votes for will have at least half of the votes, so she can claim all 50 bills.
Oh geez. You’re right. Boogers and poop!
Then Player 5 can’t let Player 4 make a proposal, or it’ll be 50/0. So Player 5 will vote for a proposal by Player 3 of 49/0/1. Knowing this, Player 4 will vote yes for any proposal Player 2 makes that gives her a bill. Player 2 will propose 49/0/1/0 and get Player 4’s vote. So neither Player 3 nor Player 5 wants Player 2 to make a proposal, so will accept a single bill from Player 1.
So Player 1 proposes 48/0/1/0/1.
Kael
1593
This is the correct answer to the riddle. But as SpoofyChop suggests it doesn’t work at all in real life where people are motivated by more than how much money they can get out of the puzzle.
Zylon
1594
I don’t see how there can possibly be a “best” answer to this, since the behavior of the other contestants is so vaguely defined. The smart response would be for everyone to vote No regardless of your plan and eliminate you from the game.
That’s why there is a qualifier that all players act perfectly rationally.
It’s no wonder these shitty questions get used at tech companies and in IT departments because this is exactly how software often gets designed :)
“Assume all software components will be very smart and behave rationally.”
We do it all the time in our IT department! I mean, why wouldn’t you design everything to work perfectly? Aren’t you a team player?
The real riddle is why people that can answer snazzy logic puzzle go on to design IT systems that suck and take three times as long to finish as the longest estimate anybody suggested.
:P
MikeJ
1597
As Dave worked out above, smart players realize that such a strategy would eventually leave all the money in the hands of the second-youngest player. So they won’t go for that…
I first heard this one as the pirate puzzle. I like it because the ‘perfectly rational’ outcome is so counter-intuitive. I guess this sort of thing is why people aren’t rational in this sense.
MattN
1598
Divide it by age and make sure the middle person gets more than 1/5 of the bills. Simple
I’d just give everybody $1,000 and call it a day. But then, I’m a pinko.
Yay, a puzzle! I haven’t read any of the other responses following this one. Here’s my guess. My assumption is that any offer has to be made in $100 increments; no change will be given.
Assuming other contestants would make rational decisions, I would propose a split of $3200 for me. Randomly selecting between the third, fourth, & fifth oldest, I would offer two of these three individuals $900 each. The proposal will pass with votes from myself & the two people I’ve offered money to.
