There was me and 4 other guys, all interviewing for the same role.

The interviewer, who I will call game master, hands all 5 of us one slip of paper each, with a positive integer written on all of them. He appeared to have distributed the slips of paper randomly.

The number he gave me was 412.

The game master asks us all to type into a computer (the 5 of us each had a comp to type stuff into) what we think the average of the 5 numbers are.

The 5 of us obv cannot talk to each other, as in no cheating.

What should I have guessed?

Results to follow.

you are trying to guess the distribution. at first i thought the only valid guess is 412, but this is wrong i think, from examining the nuanced way that distributions around N must follow.

i know this seems stupid but i think a legit likely distribution given that he is a person is that he chose numbers in 0-999. so this means that you should guess more or less (4*500 + 412)/5 = 482.4, so call it 482. if i was straight up trying to win, i would just guess that he distributed the numbers this way, and choose this*.

*however, there is another fly in the ointment, i think nash play when you are trying to guess "closest" and there are multiple players, is to guess sometimes above or below so that you win more often. so its even more complicated.

Knowing the role is important, as you would want to give an answer that best fits the role. For example, if this role was somehow circus clown, I'd guess something like "honk." But for now I'll presume this is a more serious role, along the lines of computer programmer team leader, or the like.

Since the interviewer is interested not in whether you can actually guess the number, but how you think about the best way of guessing the number, I would not just guess a number. Secondly, he probably doesn't mind if people think outside the box a little bit, so I'd probably give him an equation or a range of possible numbers. I'd probably write something along the lines of: any one of all if the real numbers from 412/5 up to (but not including, of course) infinity. If you feel really randy, you might give a list of assumptions you can make based on clues he may have given, and then narrow the field a bit.

The role is to do with financial intruments. I'd rather not be more specific as I think these guys would prefer to keep their hiring process unkown to future applicants.

Also some more info I should have added to OP is we were doing all kinds of stuff like this for hours, and in general the game master was pressuring us to put in an answer in like 5-10 seconds. So we barely had the time to type out some kind of range or something, but yeah I was pretty sure he just wanted 1 number anyway.

alex,

yeah I was thinking pretty much what you said, and guessed the game master would have a distrubution of X for the numbers, where the number of digits of X would be equally likely to be 1,2,3,..z where 3 <= z <= 7

Anyways with this in mind, and having like 5 seconds to think I just typed in 1,000 as my guess. What do you guys think so far?

edit: actually first round is kind of boring so I'll move on

I put in 1,000, and the other 4 typed in their numbers. The game master says "Okay you've all put in your numbers, I will tell you the average of your 5 guesses is 6,215"

(I can't remember the exact number but it was about 6,000)

"Now I want everyone to guess what the actual average is again. C'mon people 5 seconds."

What do we do?

In 5 seconds, you must assume that they are guessing very close to their number. So if you tweak your guess down 500, it results in a change in the average of 100.

I had the same thought proccess, but perhaps a more accurate method. I knew I overguessed by about 500, so simply knock 500/5 off of the average. My guess was therefore about 100 lower than what he quoted. So I typed in:

6,100

The game master says: "Okay guys the average of these new 5 guesses was 7,245. Everyone type in a new guess."

I think he gave us like a bit more time this time, maybe 10-15 seconds.

What do we do? And wtf why is it so much higher?

Outlier, for example a bunch of people got a number like 9123 and then guessed 5k initially. They then corrected their guess up by an average of 1k.

The point is, at this point everyone has adjusted, so you can try to compute the readjustment but we already know its going to be close to 7.2k anyways.

So you're proposing we go ~7.2k?

I wasn't really sure what to do at this point.

I'll let the US crowd wake up and have a think before i post next round's results

care to elaborate?

For one thing, there is not enough information in the OP. The interviewer cannot be handing out positive integers chosen at random, so how have they been chosen? In the absence of that information, why not 412?

We would all have to cooperate for one round yeah? And trust each other?

We didn't though, no one tried to. I suppose we were all stuck in a competitive mindset as many games we played earlier were clearly zero sum, and we were all trying to come out on top.

Also we were never told how many rounds there were going to be.

ah, i thought you meant as the 3rd guess (it's a possible answer there imo). As the first guess i agree, given Pompey's post. Guessing the given number and then the given average looks like the 'GTO play'.

To clarify the intervewer chose the 5 numbers, so yea they were not random

But he then appeared to randomly distribute the 5 numbers to each of us. So for example I knew the chance of me having the highest number was 1 in 5 (before i looked at my
number that is), assuming no duplicates

Edit: ah ok you meant first guess. Yeah i think 412 is quite reasonable.