Math Awareness Week Contest 2001

Answers

Monday: Who was the author of The Elements?
Answer: Euclid

Tuesday: This mathematician was one of the founders of computer science. During World War II, he was instrumental in breaking the German "Enigma" code. Who was he? Please give both his first and last name.
Answer: Alan Turing

Wednesday: A prime number is a whole number bigger than one that cannot be written as the product of two smaller whole numbers. For example, 15 is not prime since 15 is equal to 5 times 3. On the other hand, 11 is prime since it can only be factored as 1 times 11. What is the smallest prime number that ends with the digits: two, zero, zero, one?
Answer: 102001

Thursday: A perfect square is a number that is the product of a whole number with itself. For example, 9 which is equal to 3 times 3 is a perfect square. A triangular number is one that is the sum of consecutive integers beginning with 1. For example, 6 = 1 + 2 + 3 is a triangular number. Note that 36 is both a perfect square (36 = 6×6) and a triangular number (36 = 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8). What is the next number that is simultaneously a perfect square and a triangular number?
Answer: 1225 = 352 = 1 + 2 + 3 + ... + 49

Friday: A 10 inch cube (i.e. one whose dimensions are 10 inches by 10 inches by 10 inches) is divided into one inch cubes as shown in the figure. The surface of the larger cube is painted black. How many of the smaller cubes have none of their faces painted? How many have one face painted? Two? Three?

A 10 by 10 by 10 cube

Answer: There are 512 cubes with no faces painted, 384 cubes with (exactly) one face painted, 96 cubes with (exactly) two faces painted, and 8 cubes with three faces painted.

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