I’m on vacation with my family at Disneyworld all week this week, so we’ll do things a little differently. For those of you who aren’t spending the week at theme parks, here is another kind of recreation: two sites full of puzzles of a variety of types.
Everything you’ll find at both sites is rich in mathematical content (but feel free not to notice).
Logic Mazes, a site belonging to Richard Robert Abbott (inventor of Eleusis and other card games). What he calls logic mazes are sometimes called “mazes with rules”. For example, in the Alice mazes, you navigate a grid by following arrows, but the size of your steps changes as you pass through certain squares. So you might find it easy to get to point A with step size 2 but have to work quite hard to get the same point with step size 3. So even small-appearing mazesa can conceal vast maze structure. Many of the puzzles are playable online.
Puzzle Beast is a collection of Puzzles like no other. Perhaps most reamrkable is that the individual puzzles are generated by computer (the mathematics of how this is done is a story in itself!). If you want a suggested starting place, The Fried Okra Perplexity is good, as is the Dry Cleaning. All are original, all puzzle types include problems that will entertain and challenge any solver.
Oh, sure, there are a lot of good math topics that relate directly and indirectly to the puzzles on these sites, but we can talk about that later. Let’s not let my explanations get in the way of your own discovery. Just go play.
Posted by Cap Khoury 
. This is very different from the number line that most of us learned in kindergarten, which consisted of the counting numbers together with 0 and their negatives. There is a drastic qualitative difference between these two versions of the number line — one is continuous and one is discrete. There are measurable and noticeable gaps between the integers. It’s the difference between a ribbon of highway and the mile markers along the way.
where 
are real numbers, not both zero. (Note that this is different from how we make fractions … with fractions the denominator is never allowed to be zero, but the numerator can be; here either can be zero as long as they are not both zero.) We consider two pairs 
and 
to be the same if there is a number $\lambda$ so that 
and 
. In other words, we think of 
and 
as the same object. Likewise 
and 
are the same object. So our objects are ordered pairs modulo rescaling. Even though they look like ordered pairs and make you think of points in a plane, these really should be thought of as numbers, or points in a one-dimensional thing.
, by Paul Nahin.
