You can add location information to your Tweets, such as your city or precise location, from the web and via third-party applications. You always have the option to delete your Tweet location history. Learn more
There are 100 prisoners, numbered 1-100. The prisoners' numbers are written onto 100 cards, put randomly into 100 envelopes numbered 1-100. They can't communicate, but are invited, one by one, to open 50 envelopes. If any prisoner fails to find his number, they all get killed.
At best, there's a 50% chance any one prisoner can find his number. It would seem like there's a probability of (½)¹⁰⁰ or 0.00000000000000000000000000008% that every prisoner could find his own number, if each were to check 50 envelopes at random.
They could certainly do even worse than this. If they all agreed in advance to open envelopes 1-50, then fifty of them would be guaranteed never to find their number and they'd all die. But could they come up with a strategy in advance which would improve their survival chances?
What makes this my favourite combinatorics problem is that there *is* a strategy which increases their likelihood of survival from 0.00000000000000000000000000008% to about 30%. So, what is the strategy, and why does it work?
Can they re-arrange the envelopes? Do they see/know which numbers were in which envelopes?
They can see which numbers are in which envelopes, but they're not permitted to change the envelopes in any way which would communicate anything to the next prisoner.
This took longer than I'd like. Open the drawer w/your own matching number. If the number doesn't match, open the drawer for that number. Repeat. Now we're hoping that none of the prisoners are in a cycle of length > 50, but at least there can be only one such cycle.
Where did you originally get this problem from, out of interest.
A mathematician friend told me the problem in around 2008. It seems like it was first described in 2003, according to Wikipedia.
Okay, so there's 100 of them. Do they have something they can turn into weapons? Beds' legs? Chairs? Can they turn over mattresses to protect themselves? How many jailers are there and what weapons do they have?
#thinkingoutsidethebox
Twitter may be over capacity or experiencing a momentary hiccup. Try again or visit Twitter Status for more information.
