number-theoretic "games"

[Sara L. Uckelman]

Tonight at supper my partner introduced our 9yo to the Collatz 
Conjecture.  She had so much fun with this "game" that it made me wonder 
what other sorts of number theoretic results/conjectures/algorithms 
would similarly be fun for a child who insists her favorite subject is 
maths and hasn't yet been told that math isn't fun or isn't for girls.

We've done the Sieve of Eratosthenes before, which was a hit, and prime 
factorization, which wasn't.

Number theory is so often presented as a rarified subject that you only 
get in grad school and only certain nerds want to specialise in, and yet 
number theory has always struck me as exactly the sort of thing we 
should be introducing to children at quite a young age because from 
their perspective, it really is just a game.  It strikes me that there's 
potentially a niche out there to be filled by a book geared at primary 
school children introducing them to important number-theoretic results 
and conjectures by formulating them as a type of game.

So, what sorts of results/conjectures would you want to see in such a book?

Cheers,
-Sara

-- 
Dr. Sara L. Uckelman
Department of Philosophy
Durham University
http://community.dur.ac.uk/s.l.uckelman/

The Dictionary of Medieval Names from European Sources
http://dmnes.org/