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More ways to get Braingle...

Prime Nine

Probability puzzles require you to weigh all the possibilities and pick the most likely outcome.

 

Puzzle ID:#40004
Fun:*** (2.56)
Difficulty:** (2.01)
Category:Probability
Submitted By:RampaginRoboAgb*****!

 

 

 



There are 9! ways to arrange the digits 1-9 to form a 9-digit number.

E.g. 345, 987, 126

If you know this, then if I wrote all 9! possibilities on cards (1 way per card), and I asked you to select one at random; what is the probability that the number you selected is prime?





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Comments

ScubeeAus*
Jan 11, 2008

9 ways to arrange the digits 1-9 to form a 9-digit number?

I'm confused. If my calculations are correct, wouldn't there be 362880 (9*8*7*6*5*4*3*2*1) possible ways to arrange 1-9 into a nine digit number? This doesn't change the answer but confusing still.
RampaginRoboAgb*
Jan 11, 2008

Scubee, 9! means 9 factorial which is 362, 880.
Holoten*
Jan 12, 2008

Actually, there would be 3,486,784,401 ways
calmsaviorAus*
Jan 13, 2008

Congratulations on having the first approved teaser with a 4 in the ten-thousands position.
RampaginRoboAgb*
Jan 20, 2008

Firstly, thanks calmsavior! And secondly, where did your idea come from Holo?
bookwrmKPAus*
Feb 01, 2008

Wow. I would have never figured that out.... I guess I'm not as smart as you guys... Very clever!
jsdodgersAus*
Apr 03, 2008

One problem. 9! means 9*8*7*6*5*4*3*2*1, not 9+8+7+6+5+4+3+2+1.
jsdodgersAus*
Apr 03, 2008

Nevermind my last comment. I understand where you got the 9+8+7+6+5+4+3+2+1 from now.
scott8anthony
Apr 11, 2008

I must say this one incorporates a simple rule and disguises it very well; good job!
stephiesd**
May 03, 2008

Whoo. This teaser was amazing. It actually took me a minute...

But then I got it. (With the hint... )
Lord_HawkAsx*
Jan 04, 2009

I like the way this simple problem disguises such a simple division rule. It took me a while to notice it. I must boast that I didn't have to look at the hint though
opqpop
Sep 27, 2010

Too easy.

Which numbers are prime? Oh look, 1+...+9 = 45 which is divisible by 3 and you're done.
daquity36
Jun 25, 2012

This problem seems incorrect.. What about #'s such as 127, 137, 149, 157 ... etc?
http://en.wikipedia.org/wiki/List_of_prime_numbers
daquity36
Jun 25, 2012

Oops never mind. I thought this problem was for 3 digits.



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