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Post by Minyahil on Mar 16, 2009 18:50:25 GMT -5
Answer a number or logic related question, pose one of your own, or preferably both. Here's one to start:
What are the last two digits of (2^2009 * 3^2009)^2009?
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Post by CyMoahk on Mar 24, 2009 15:59:17 GMT -5
56 lol That looks like it came straight from a 2009 version from the AMC test series. ^.^
Here's one that is straight from 2009, thanks to one of my friends still in high school: Rachel and Robert run on a circular track. Rachel runs counterclockwise and completes a lap every 90 seconds, and Robert runs clockwise and completes a lap every 80 seconds. Both start from the start line at the same time. At some random time between 10 minutes and 11 minutes after they begin to run, a photographer standing inside the track takes a picture that shows one-fourth of the track, centered on the starting line. What is the probability that both Rachel and Robert are in the picture?
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Post by Minyahil on Jul 29, 2009 22:00:01 GMT -5
I'm getting 1/96, with Rachel leaving just as Robert's getting there. Someone feel free to check me though.
A randomly chosen six-digit number contains at least one each of the digits 1, 3, 5, 7, and 9. What is the probability the other digit is even? (And no, it's not 1/2)
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Post by CyMoahk on Jul 31, 2009 19:15:08 GMT -5
Question: are first digits allowed to be zero for this problem? Or are we starting "six-digit numbers" at 100000?
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Post by Minyahil on Jul 31, 2009 22:30:30 GMT -5
Good question. 0's are fine-- "sequence of six digits" would probably have been better.
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Post by CyMoahk on Aug 3, 2009 21:07:59 GMT -5
Okay, then. I'm getting 2/3 - 3600 numbers where the unknown digit is even and 1800 where it's odd - the reason why it's not 1/2 is because you have to be careful to not count numbers like 137359 twice.
The Malach Nationals have made it to the World Series once again as Red League champions, as expected. The surprise this year is the upset of the Task Angels sweeping the Ra'isse Warriors to become the Blue League champions. Still, most people favor the Nationals to win the series, with the consensus being that the Nationals have a 2/3 chance of beating the Angels in any one game. What is the expected length of the best-of-seven series if the Angels pull another upset?
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Post by Minyahil on Aug 3, 2009 21:33:52 GMT -5
You mean, given that the angels end up winning?
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Post by CyMoahk on Aug 3, 2009 22:21:04 GMT -5
yeah, I guess ^.^''
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