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  #61  
Old Nov 5th 2008, 12:09 AM
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dilettante dilettante is offline
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Default Re: Brain Teasers & Riddles

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Originally Posted by Michael View Post
Okay, looks like Dilettante gets the credit here (and moves into the lead on the scoreboard!).

You're up.
Hmmm...I'm not sure I deserve credit for that one, but I'll go ahead and post another brain teaser:

Quote:
Odometers on modern cars go from 0 to 999,999. There are no tenths; all the tenths are done by the trip odometer.

Imagine that someone managed to reach 999,999 miles. If you counted all the times that the digit 1 appeared, how many 1s would be counted? In doing this, count each time that 1 appears in a number.
So, for example, from 000,000 through 000,012 the count would be 4: 1 for 000,001, another for 000,010, two more for 000,011 and another for 000,012.
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  #62  
Old Nov 5th 2008, 12:36 AM
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Default Re: Brain Teasers & Riddles

600,000 ?
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  #63  
Old Nov 5th 2008, 08:28 AM
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Default Re: Brain Teasers & Riddles

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600,000 ?
Correct! Your turn.
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  #64  
Old Nov 5th 2008, 10:14 AM
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Default Re: Brain Teasers & Riddles

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Hmmm...I'm not sure I deserve credit for that one, but I'll go ahead and post another brain teaser:
Yeah, it was a bit unclear, but yours seemed closest.
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  #65  
Old Nov 7th 2008, 06:24 PM
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Default Re: Brain Teasers & Riddles

Once again, I'm invoking the 24 hour rule.

Next challenge:

There are 25 horses and the race track only allows 5 horses to race at a given time. Given that there is no stop watch available your task is to determine the fastest 3 horses. Assume that each horses' speed is constant in different races, what is the minimum number of races to determine the fastest 3?
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  #66  
Old Nov 7th 2008, 07:13 PM
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Default Re: Brain Teasers & Riddles

Oooh, comptuer science... lol.

Eight races.
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  #67  
Old Nov 7th 2008, 07:25 PM
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Default Re: Brain Teasers & Riddles

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Oooh, comptuer science... lol.

Eight races.
Not correct.

There is a way to do it with less. You work for Microsoft or something?
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  #68  
Old Nov 7th 2008, 07:36 PM
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Default Re: Brain Teasers & Riddles

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Not correct.

There is a way to do it with less. You work for Microsoft or something?
Nah. Since it has to be between five and eight, I'd imagine the Microsoft answer would be somewhere around 15.

My answer was the product of modified "merge sort" (though, merge sort is not always optimal, as we're apparently seeing here... )
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  #69  
Old Nov 7th 2008, 07:43 PM
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Default Re: Brain Teasers & Riddles

Oh, scratch it. I know the answer, but I won't say, since I already screwed the pooch. I shouldn't have been using any sorting at all...

I arrived at the answer I did by thinking of the maximum number that you could eliminate in any given race - for the first five races, you eliminate two each for a total of fifteen. Then, you can eliminate 4 horses in each subsequent race for a total of 11, then 7, then 3 horses remaining after 8 races. I figured I had to be right since the math lined up so nicely. Thinking man's error - life isn't a standardized test
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  #70  
Old Nov 7th 2008, 08:28 PM
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Default Re: Brain Teasers & Riddles

I can get it down to 7.

Races 1-5: Divide horses into sets of 5 (A-E) and race them, eliminate all fourth and fifth place finishers immediately. We can now rank the 3 remaining horses of each group internally.- down to 15 horses.

Race 6: Race the winners of the first 5 races. Lets say the winner of group A places first, the winner of group B second, the winner of group C third...etc. Eliminate groups D and E entirely. Eliminate all but the fastest horse (the one who just raced) in group C. - down to 7 horses.

We know the winner of the last race (the fastest in group A) is THE fastest horse, so we can set him aside; now we just need to find the other two. We also know that the slowest horse of the 3 in group B cannot be among the 3 fastest, so we eliminate him. That gives us 5 horses left to race.

Race 7: Race those five (the 2nd and 3rd place finishers from group A, the 1st and 2nd place finishers from group B, and the only remaining horse in group C). The top two finishers and the horse we set aside earlier are the 3 fastest.
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