Published: Thursday, October 3, 1991 Section: VIEWPOINT Page: 13A

Alison has an incredible coin machine. When she puts in a nickel, it gives back 5 pennies, and when she puts in a penny, it gives back 5 nickels. If she starts with just one penny, is it possible that by repeatedly using the machine she will eventually have the same number of pennies as nickels?

A nation of couch potatoes can continue to enjoy sports on TV as long as there are enough talented kids willing to spend their afternoons and weekends honing their skills for the NBA and NFL. And maybe a nation of mental couch potatoes can count on having the satellites, televisions and fiber optic networks to bring the sports as long as there are enough bright kids willing to spend their afternoons and weekends honing their math and technological skills to be the scientists and engineers of tomorrow. The difficulty, judging from this week`s reports about national math achievement, is that very few American youngsters are doing that. The scores suggest that we will have plenty of math couch potatoes, but very few math and science stars (and not many who would even qualify for Saturday afternoon pickup games). Nationally, the top ranking of ``advanced`` was earned by only 2.6 percent of high school seniors, 1 percent of eighth graders and less than 1 percent of fourth graders.

Abbie has three cards: one red on both sides, one blue on both sides, and one red on one side and blue on the other. One card is selected at random and one side of it is examined. What is the probability that the other side is the same color as the first?

It would be comforting to think that the fault lies in the test and the standards. After all, the stories said that today`s students actually were doing, on average, about as well as their counterparts two decades ago - back toward the days when we were taking the tests. But the world has moved on. The issue isn't whether our students are as good as we were, but whether they are as good as today`s competition in places like Japan and Germany. Sadly, they're not, according to international examinations.

The letters A,B,C,D,E,F stand for the digits 0,1,2,4,6 and 8 (but not necessarily in that order). Now suppose that AB, CD and EF are two digit numbers such that EF - CD=AB. Find the digit that E represents.

One place to address the nation's math shortcomings is the schools, which face a massive job in moving the 80 percent-85 percent of American students who fell below the ``proficient`` rating used to signify good, solid, on-grade achievement. Think of that effort as the academic equivalent of school phys ed, designed get everyone off the couch a little bit. But if we wanted to strengthen our future Olympic teams, we wouldn't stop with phys-ed classes. We'd also look to the playgrounds, and create ways for talented kids to develop outside class. In math, the schools do some of that with programs like MathCounts, Superstars and math field day.

UNC Charlotte`s Dr. Harold Reiter, with the support of the UNCC Math-Science Education Center, does it with once-a-month Saturday math clubs, which will start up for the year Saturday, Oct. 12 (grades 4-6, from 9:30-12 at Merry Oaks) and Saturday, Oct. 19 (for junior high, from 9:30-12 at Providence Day). They`re not tutoring sessions for kids who would rather be elsewhere. Nor are they drill and lecture, or advanced classes for students wanting to scoot up the academic ladder. The one I went to last spring, in fact, was like the all-out scrimmage my daughter's soccer team and coach were romping through Tuesday. For kids who think solving math problems is a fun way to spend a Saturday morning, these sessions are a chance to play and grow. America's dismissive mythology aside, math can be fun. When we ran an editorial about Marilyn vos Savant and the ``Monty Hall Dilemma,`` we got a small flood of letters arguing the case back and forth. I asked Reiter to suggest some more problems that readers might enjoy, the way many enjoy our crossword puzzles and scrambled word problems.

He sent seven, and I got five more or less right (right answer, but incomplete reasoning). I had fun, and thought maybe some of you would too. So I have scattered three of them through this column. While Reiter, a math professor, was able to show some nifty shortcuts to the answers, none requires higher math. I used the equivalent of counting on my toes and fingers: making tables to list possibilities, for example. The coin machine and the red-blue cards both lend themselves to simulations (say, poker chips or coins for pennies and nickels, and marked squares of paper for the red and blue cards.) I'll print the answers Tuesday. And if your kids think this sort of thing is fun (even if they stumble on these problems), you can learn more about the math clubs by calling Harold Reiter (547-4561) or Jean and Rudolph Worsley at the math center (547-4859). Ironically, this week`s reminder of our mediocrity in math came just after the embarrassment over our superiority in basketball. A lot of us argued that it would be unsporting to send our best - our NBA players - to represent us in Olympic basketball. They`re too dominant. Wouldn't it be better if we had to worry that we were too dominant in math as well? Tom Bradbury is an Observer associate editor.

\ THOUGH THEY AREN`T AS COMMON, MATH PUZZLES CAN BE AS TANTALIZING AS WORD GAMES AND CROSSWORD PUZZLES Published: Tuesday, October 8, 1991 Section: VIEWPOINT Page: 11A By Tom Bradbury, Associate Editor As promised, here are the answers to the three math puzzlers from UNC Charlotte`s Dr. Harold Reiter that I posed last Thursday (``Help America's math stars shine``):

Alison has an incredible coin machine. When she puts in a nickel, it gives back 5 pennies, and when she puts in a penny, it gives back 5 nickels. If she starts with just one penny, is it possible that by repeatedly using the machine she will eventually have the same number of pennies as nickels? Alison may get rich turning pennies into nickels, but the coin machine will never leave her with the same number of pennies and nickels. Why? * Each time she uses the machine, she loses one coin (the one she put in) and gets five back. Each turn thus leaves her with four more coins than she started with. So her stock of coins goes from 1 to 5 to 9 to 13 etc. * Notice that those are all odd numbers. Each turn adds four coins (an even number), but does not change whether the total is odd or even. Since Alison started with an odd number, she will always have an odd number. * But if she had the same number of pennies and nickels, she would have an even number of coins. Since she will never have an even number, she can't have equal numbers of pennies and nickels. * Or, to use a little math notation for compactness, let n+p denote the number of nickels and pennies. The original total is 0+1. The total increases by 4 each time. Adding an even number - such as 4 - does not change a total from odd to even. If n+p is odd to begin with, it will always be odd. * I wonder: Does starting with an even number of coins guarantee a match? If not, is there any particular number of coins that will produce a match?

Abbie has three cards: one red on both sides, one blue on both sides, and one red on one side and blue on the other. One card is selected at random and one side of it is examined. What is the probability that the other side is the same color as the first? The answer is -2/3. She has three choices: the all-blue card (both sides the same), the all-red card (both sides the same) or the red-blue card (two sides different). In two of the three choices, both sides are the same. In only one of the choices (the red-blue card) is the hidden side different. Therefore, the chances of getting a card with a matching backside are two out of the three; in math talk, the probability is -2/3. The letters A,B,C,D,E,F stand for the digits 0,1,2,4,6 and 8 (but not necessarily in that order). Now suppose that AB, CD and EF are two-digit numbers such that EF - CD= AB. Find the digit that E represents. The starting point is to look at the shape of the equation - no three-digit numbers - and the available digits (no repetitions, and only one is odd). Reiter first simplified things a little by converting the problem from subtraction (EF - CD= AB) to addition (AB + CD= EF). That's legal, of course. Then he homed in on the fact that the available digits contained only a single odd number. The only way to have just a lone odd number in an addition problem is to have a carry to add to it, thus producing an even result. So in this case the odd number - the 1 - has to go in the left column as either A or C. For the moment, then, let A=1. To produce the carry, B + D must be 10 or greater. If A=1, then E=C + 2. This can only happen if C=4, E=6 and B and D are 2 and 8 in some order. So the answer to the question is that E=6 (and, as it happens, F=0). Although we assumed A 1 in order to work to a solution, we could have let C=1. So we can't determine what A,B,C and D are: 42 + 18=60 and 12 + 48=60. Reiter and I attacked the problem differently. I started by deciding that the 0 had to go in the right column (by custom, if not mathematical necessity). I, too, ended up with E 6. A confession, however: I grabbed the first solution that worked - and didn't notice till I saw Reiter's explanation that we really don't know what A,B,C and D are. Fortunately, the question only asked about E, which I got. On a multiple-choice test, I get it completely right. On a show-your-work test, maybe I lose points for incompleteness.

Though less common than newspaper crossword puzzles and word games, math puzzles are equally tantalizing. Their value for kids is not only that they sharpen skills, but that they give a glimpse of the fun and the power that lie beyond math`s necessary but tedious facts and formulas. The schools offer a number of math-can-be-fun activities. And as I noted in the first column, Reiter leads a pair of children`s math clubs with the support of the UNCC Math-Science Education Center. They`re not for kids who would rather be elsewhere, nor drill and lecture for kids wanting to boost their test scores. But for kids who find math exhilarating and think solving mathematical brain twisters is a neat way to spend one Saturday morning a month, the clubs offer a lively challenge. The sessions start up this month. The club for grades 4-6 is this Saturday, Oct. 12, from 9:30-12 at Merry Oaks Elementary. The junior high club is the following Saturday, Oct. 19, from 9:30-12 at Providence Day. For information, call Harold Reiter (547-4561) or Jean and Rudolph Worsley at the math center (547-4859).