Some doctors use body-mass index (BMI) as a health risk indicator. According to The Old Farmer's Almanac 2000, BMI can be found using the formula: BMI = [(W×705)÷H]/H, where H is height in inches and W is weight is pounds. An index greater than 27 or less than 19 indicates an increased risk for health problems. Helix is 5 feet, 2 inches tall and weighs 110 pounds. Is his health at risk?

In May 1999, two National League baseball players, Joe McEwing of the St.Louis Cardinals and Mike Lieberthal of the Philadelphia Phillies, each had the batting averages, as show below.

Lieberthal: Bats- 132; Hits- 45; Batting Average- 0.341

McEwing: Bats- 132; Hits- 45; Batting Average- 0.341

Suppose McEwing then batted 0.800 (4 hits in 5 at bats), and Lieberthal was perfect (3 hits in 3 at bats). Which player now has the higher batting average? Are you surprised?

Imagine that you bought a Beanie Baby® for $6, sold it for $7, bought it back for $8, then sold it for $9. How much profit did you make?

The Environmental Protection Agency (EPA) estimates for gas mileage on 1999 cars vary widely. Which of these cars should go the farthest on one tank of gas?

If each side of the triangle in Figure 1 is 1 inch long, this means the triangle has a perimeter of 3 inches. Suppose you continued the pattern in the diagram until you reached Figure 5. What is the sum of the perimeters of all the white triangles in Figure 5?

Suppose you love chocolate. The top of each cookie is covered with the same thickness of chocolate. If you wanted to choose the cookie with more chocolate, which would you pick?

Mark McGwire became baseball's home run king in 1998 with 70 home runs. His 70th home run ball sold for slightly more than $3 million in 1999. Babe Ruth, an earlier home-run king, hit 60 in 1927. His home-run ball was donated to the Hall of Fame. Suppose that Ruth's ball was valued at $3000 in 1927 and, like many good investments, doubled its value every seven years. Would you rather have the value of Ruth's ball or McGwire's?

Take two sheets of 8.5 by 11 inch paper. Roll one into a short cylinder and the other into a tall cylinder. Does one hold more than the other?

Two players each roll an ordinary six-sided die. Of the two numbers showing, the smaller is subtracted from the larger. If the difference is 0, 1, or 2, player A gets 1 points. If the difference is 3, 4, or 5, Player B gets 1 point. The game ends after 12 rounds. The player with the most points wins the game. Is the game fair?

If all grape juice concentrates are the same strength, which recipe would you expect to have the strongest grape taste?

Suppose you found an old roll of 15¢ stamps. Can you use a combination of 33¢ stamps and 15¢ stamps to mail a package for exactly $1.77?

Every year, Arctic terns fly from the Arctic to the Antarctic and back, a distance of about 9000 miles each way. Suppose the birds fly at an average speed of 25 miles per hour for 12 hours a day. How many days of flying would be necessary to make the roundtrip?

Would you rather work seven days at $20 per day or be paid $2 the first day and have your salary double every day for a week?

Your team is down by one point. Your teammate, who makes free throws about three-fourths of the time, is at the free throw line. She gets a second shot if she makes the first one. Each free throw she makes is worth 1 point. If there is no time left, what are the chances you win the game without overtime?

Mara has 3 times as many dollars as her brother, Timmy. If Mara is given $20 by their mother, she will have 7 times as many dollars as Timmy. How many dollars does Timmy have?

Juliet bought 10 beads for $18. The beads she bought are red, blue or silver. Red beads are $1 each, blue beads are $2 each and silver beads are $5 each.  If she bought at least one of each, how many red beads did she buy?

A rectangular wooden block (not necessarily a cube) is painted on the outside and then divided into one-unit cubes. It turns out that exactly half of the cubes have paint on them. What were the dimensions of the block before it was painted?

In each of the following 5 boxes, there are some letter cards. Joseph takes exactly one letter card out of each box and spells the word ‘QUEST’. Which letter card did he take out from Box 4?

In the Sudoku grid at left, only the numbers along the perimeter are shown.

Suppose the grid was completed according to the standard Sudoku rules — each row, column and 3 × 3 square contains the numbers 1–9. Would the sum of all the missing numbers be divisible by 3?

In our Mathematics Circle we diagrammed 16 blocks of our city. How many different routes can we draw from A to C moving only upward and to the right?”

Different routes may, of course, have portions that coincide (as in the diagram).

“This problem is not easy. Have we solved it by counting 70 different routes?”

What answer should we give these students?