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## Thursday, August 21, 2014

### And a Few More Puzzles

If the prior puzzle was a bit too much for you, a few below that are more manageable...

Been reading "Mathematical Curiosities," new from Alfred Posamentier and Ingmar Lehmann. It is, as the subtitle suggests, "a treasure trove of unexpected entertainments" -- especially entertaining if you have a geometry bias.

In the middle of it come 90 "curious problems with curious solutions." Several of these are classics with which you'll be familiar, and others are a little fresher, all interesting. I'll pass along three to whet your appetite (these are paraphrased from the volume):

#1.  I feel like EVERYone should know this first one, so just passing it along for any readers not already familiar with it:
On a certain pond the water lilies double in number every single day. After the 50th day the pond is completely covered. How many days were required for the pond to be half-covered?

#2. Given the following four numbers:

8,932
12,668
85,423
9,165

What percentage of their sum, is their average?

#3. What time is it now if in 2 hours it will be one-half as long 'til noontime as in 1 hour from now?

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1)  49 days

2)  25%  (if you work this out the 'long' way, you may then see there's an easier, more general solution)
3)   9 am.