[plt-scheme] mathematicians lament

Jon Rafkind wrote:
> http://www.maa.org/devlin/LockhartsLament.pdf
> 
> This is a comment on the state of teaching mathematics. I'm not sure how 
> old it is but a few parallels can probably be drawn to computer science 
> (or maybe will be drawn in a few years). The first 3 pages are pretty 
> amusing, at least.

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.

Last month we had a great discussion about the "Ten in the Bed" song. 
("... then the little one said, 'Move over! move over!' So they all 
rolled over and one fell off...") I helped them through a (not at all 
rigorous) inductive proof that no matter how many kids started in the 
bed ("a million kids!"), the bed always ends up empty. We've defined 
infinity as the number of toys in a box where, if you take a toy out of 
it, I can always find a bigger toy in it.

These have been some of the liveliest discussions, and I'm looking for 
source material.

Neil T