Odd odometer reading matched at checkout

We are wondering: Is there any way to figure the odds of the numbers coming up like this?"

A: There are lots of possible assumptions and answers, suggests University of California-Los Angeles mathematician James Ralston.

For example, ignoring the decimal and assuming all five-digit numbers between 10000 ($100.00) and 99999 ($999.99) are equally likely, the chance is 1 in 90,000, since there are 90,000 such numbers.

If you broaden this to include the UNLIKELIHOOD of spotting the 22,222 on the odometer, things get even more interesting. Let's call these "monodigital" readings, says College of Charleston mathematician Alex Kasman. The probability of spotting one of these at any given time is small. Starting out, a car runs through 11 miles, 22, 33 ... 111, 222, 333 ... and so on. Drive 100,000 miles and you'll turn over 36 monodigitals. "They're certain to occur, though you probably won't notice most of them."

If you spend $10 to $1000, there are four monodigitals — $22, $22.22, $222 and $222.22 out of 99,001 possible prices — to match 22,222 miles. Thus the probability is 4/99,001, or just a bit more than a one-in-25,000 chance.

Probably the game will drive you crazy first ....

Q: Why is ice so slippery? Better watch your step on this one ... (a) pressure melting puts water underfoot, (b) frictional heating under skis or skates creates the glide, (c) it's just ice's icy nature

A: (a) and (b) used to be given, but it's now known that the pressure under a walker's boots or the friction of skate blades against ice doesn't play much of a role in melting, reports Physics Today.