The winner was Lanie Deng, a 10th grade student at Central HS in Springfield, MO, and the runner-up was Brad Meyer, who works for Ozarks Public Television. Jackson Frieze, a math major here at MSU, also answered all five questions correctly. Well done!
Monday
This year is the centennial of the birth of this French mathematician (who is still alive). He made seminal contributions to algebraic topology, algebraic geometry, and algebraic number theory. He was awarded the Fields Medal in 1954 and the first Abel Prize in 2003.
Who is he?
Answer: Jean-Pierre Serre
Tuesday
For a positive intger n, n! ("n factorial") is the product of all the integers from 1 to n inclusive. For example, 4! = 1·2·3·4 = 24. How many (decimal) digits does 2026! have?
Answer: 5822 digits
Wednesday
A fair (standard) six-sided die is tossed four times. What is the probability that at a 1 or a 2 appears at least once?
Answer: 65/81 or approximately .80247
Thursday
Let f (n) denote the number of ways of tiling an n×1 rectangle with 1×1, 2×1, and 3×1 rectangles. For example, the figure below shows that f (4) = 7. Find f (10).
Answer: There are 274 tilings.
Friday
The large octagons in the figure are regular and congruent. What is the ratio of the area of the larger shaded octagon on the left to the area of the smaller shaded octagon on the right?
Note: Take time to verify your answer. An incorrect answer will receive a reply and a chance to resubmit, but there will be a delay to allow others to submit their answers. A maximum of four incorrect answers per contestant is allowed.
Answer: The ratio of the areas is (2+√2):1.
Read more information about Mathematics and Statistics Awareness Month.