# [plt-scheme] mathematicians lament

 From: Jordan Johnson (jmj at fellowhuman.com) Date: Fri Nov 20 14:20:33 EST 2009 Previous message: [plt-scheme] mathematicians lament Next message: [plt-scheme] #%app literal does not match in syntax-case pattern Messages sorted by: [date] [thread] [subject] [author]

```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-
oriented.

Best,
Jordan

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?
>
> _________________________________________________