[plt-scheme] mathematicians lament

From: Jordan Johnson (jmj at fellowhuman.com)
Date: Fri Nov 20 14:20:33 EST 2009

Another good one is the mutilated checkerboard problem: can you tile a  
checkerboard with 1x2 dominoes if two diagonally opposed squares have  
been removed?

It's a great introduction to the concept of proof:  visually and  
kinesthetically accessible, with a very simple but non-obvious  
solution.  Usually my students get sufficiently engaged with it that  
they really want to know for sure if it's impossible.

Hofstadter's MIU-puzzle is similar in spirit but much more language- 


On Nov 19, 2009, at 5:10 PM, Stephen Bloch <sbloch at adelphi.edu> wrote:

> On Nov 19, 2009, at 4:59 PM, Neil Toronto wrote:
>> Jon Rafkind wrote:
>>> http://www.maa.org/devlin/LockhartsLament.pdf
>> Does anybody know of a list of example problems like the ones he  
>> gives in the essay? I'd love to have a big list of math teasers to  
>> draw from for dinner conversation with my kids.
> Well, you could take a look at "CS Unplugged".
> Of course there are Fibonacci numbers.  How much bigger is each  
> Fibonacci number than the previous one?  The ratio seems to be  
> alternating bigger and smaller, but the "bigger" and "smaller" are  
> getting closer to one another.  Where will they meet?  Is this  
> number interesting in any other ways?  What if I started the  
> Fibonacci sequence with something other than 1 and 1?
> Use your calculator (or, better yet, DrScheme) to write various  
> fractions in decimal.  Some of them end after a fixed number of  
> digits, while others repeat digits indefinitely.  Which are which?   
> 1/9 repeats a single digit forever; 1/11 repeats a pair of digits  
> forever; 1/7 repeats six digits forever.  Can you predict, given the  
> number n, whether 1/n will be repeating, and if so, how many digits  
> will be in the repeating pattern?  What if you write it in a base  
> other than ten?
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