Earlier this month, the Mathematical Sciences Research Institute of Berkeley outfitted San Francisco Muni buses with the first in a series of puzzles designed to pique the interest of middle school- to high school-age students and anyone else in transit.

The puzzles appear amid the mini-billboard ads above the windows and below the ceiling on the buses. They are called "Puzzles on Wheels,'' and MSRI will post a new one each month through February. October's puzzle is a square with a four-by-four grid of squares inside it. Commuters are asked to count the total possible number of squares.

Rather than opting for mind-numbing word problems straight out of a junior high school algebra textbook, MSRI's wizards decided to go with puzzles because they're more user-friendly.

"People like puzzles. Crossword puzzles. Math puzzles. All sorts of things. Puzzles don't sound very threatening. Math problems sound like death, '' said MSRI's Deputy Director Matt Miller, a math professor at the University of South Carolina on loan to the Institute through December. "What we're trying to do is to present stuff that doesn't look like school curriculum -- that they start afresh.''

Answers may be submitted to MSRI's Web site (www.msri.org). Each month a randomly selected correct respondent will receive a $100 prize. The answer to the previous month's puzzle will be posted after the new puzzle goes up. Just in case you need a little time to think about the puzzle, the billboards will also feature little tear-off slips with the puzzle on it so you can ponder it at your leisure. Four hundred of the billboards -- called bus cards -- were designed for free by San Francisco ad agency Goodby, Silverstein and Partners. They will appear on 200 buses.

Doing fairly simple puzzles are the tip of the math iceberg and can lead to an exploration of more sophisticated math problems, Miller said. With the square stumper, he says one could get the correct answer by tracing squares over the grid in as many possible configurations and counting them up.

"But now imagine that it was a 100 by 100 grid of boxes instead of four by four? Well, you're not really going to do that one by hand because how do you know you haven't missed a couple somewhere or a few dozen maybe,'' Miller said.

To get participants interested in thinking about the broader math concepts involved in the puzzles, MSRI's Web site provides a link on its page called "Taking It Further.''

With the square conundrum, Miller says a math concept that could come up is enumerative combinatorics.

"That's just a fancy way of saying sophisticated counting,'' he said. "Enumeration is counting. And combinatorics is how are things arranged, basically. How do you find a pattern to the things you want to count up to make the counting easy? If you're lucky you can maybe even develop a formula and, bingo, the formula will pop out an answer no matter what size you have.''

According to Miller, these math skills are an "important part of real active mathematics today, especially with all of this latest genomes research. ''

Another goal of Puzzles on Wheels is to get students and others on the wrong side of the so-called "digital divide,'' to go to libraries and other facilities where they can log on to answer the questions.

"We're interested in reaching people who don't have computers at their fingertips to go browsing,'' said Miller.

For high school math teacher Sandie Gilliam, using puzzles to get students interested in math is a no-brainer. A teacher at San Lorenzo Valley High School in Felton (north of Santa Cruz) for the past 22 years, Gilliam won the Presidential Award for excellence in high school math teaching in 2000 and is a fellow at the Carnegie Foundation for the Advancement of Teaching in Palo Alto. She uses the same square puzzle in her algebra classes.

"It's absolutely the beginnings of algebra if you can look at the patterns and generate a formula. These puzzles create a visual connection between something you understand and the abstractness of algebra. If we can take something and visually make the connections then the kids begin to understand."

Gilliam views an increase in math education levels as crucial, especially in understanding the graphs and charts associated with government budgets.

"We have a nation of people with math woes. They have such stories about how math was not fun,'' Gilliam said. "They never tell me history was their least favorite subject. It makes me very sad. Math is one of those subjects that helps make an informed citizenry.''

"Puzzles on Wheels'' is a pilot program with a budget of $24,000, but Miller says he'd like to see it expand. "Why just buses? Why not ultimately Southwest Airlines?''

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