25 racecars

You'll want a pencil and some paper to work out this week's "Problem Of The Week".

You have 25 remote control race cars that each travel at a consistent speed, but all travel at different speeds.  You need to determine which 3 race cars are the fastest by racing them against each other.  You can only race a maximum of 5 cars at a time.  What is the LEAST number of races you will need to conduct in order to determine which 3 cars are the fastest?

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SOLUTION FROM LAST WEEK:

Here is one possible solution ... did you come up with a different one?

You start both hourglasses off at the same time.  Once the 7 minute hourglass runs out of sand, you turn the 11 minute hourglass over on its side to stop the sand.  This leaves 4 minutes of sand left in the 11 minute hourglass.  You now turn over the 7 minute hourglass at the same time as you are turning the 11 minute hourglass back up (with the 4 minutes worth of sand at the top).  After those 4 minutes of remaining sand pass through the 11 minute hourglass, you turn the 7 minute hourglass on its side.  You are now ready to time the 15 minutes that you need.  To time 15 minutes exactly, you simply start the 11 minute hourglass.  As soon as the sand runs out (which means 11 minutes have passed), you turn the 7 minute hourglass up, making sure that there is more sand on top (because this would give you 4 minutes of sand on the top -- remember, we stopped it after 4 minutes, so half the hourglass has 3 minutes of sand, and the other half has 4 minutes of sand).  After those 4 minutes of sand have run out, you will have successfully timed exactly 15 minutes.