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