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Idk....I've no idea at all :/

Use Bayes' Theorem!

Bayes????????

what is the most likely number that 100 guys would pick?

1 ?

Not getting it..........

good! so if 100 guys pick one, then the result would be 2/3!

so if you picked 1, then you would be winning

alright, try having all guys pick different numbers: guy 1 pick 1, guy 2 pick 2... guy 100 pick 100

find\[\sum_{i=1}^{100}i\]

this is \[\frac{100*(100+1)}{2}=10100/2 = 5050\]

i did smth like
|dw:1317896959755:dw|

yes!

hmm....

|dw:1317897551125:dw|

yep, I got the same 33.3 answer after 10000 trials