[plt-scheme] mathematicians lament
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?
>
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