Games Online Contest #23

5 First Prizes: A one-year subscription to GAMES

This contest closed on July 15, 2009. A new contest will appear soon.
Here was the challenge:


Orderly Calculations

Each lettered clue below (a through o) defines a real number that is to be expressed in base 10.

a. The arithmetic average of the Roman numerals M, D, C, L, X, V, and I.

b. The positive square root of the ZIP code of Russell, MN.

c. 0 degrees Fahrenheit, in degrees Celsius.

d. The fraction of the Earth’s surface that is covered by water.

e. The two-digit positive integer n that, when its digits are reversed, is equal to 2n – 1.

f. The latitude in degrees North, rounded off to the nearest degree, of the U.S. state capital that has the highest altitude.

g. The 52nd prime number, if 2 is the first prime, 3 is the second prime, etc.

h. One percent of the square of 42i, where i = the square root of –1.

i. Number of different legal moves a player may choose from in the starting position in a game of shogi.

j. If the first four cards dealt to a poker player are the 6, 7, 8, and 9 of hearts, the probability that the player will have a pair or better (e.g., a pair, a straight, a flush, or a straight flush) after being dealt one more card.

k. Point value of a cribbage hand consisting of four 5’s and a queen.

l. Number of vowels that appear on this Web page.

m. Age, to the nearest whole year, of the oldest living Oscar-winning actor or actress (in either a leading or supporting role).

n. Probability of throwing an even number on a fair six-sided die if the last 100 numbers thrown with that die were all odd.

o. Area of Vatican City in square miles.

The challenge was to list the 15 answer letters (a through o) in order so that the numbers they define go from highest to lowest. It was not necessary to list the values of the answers.

Answers

From high to low, the order is: l, g, a, b, m, e, f, i, k, d, j, n, o, h, c. Explanations follow.

l. Number of vowels that appear on this Web page. [More than 239, which is all that is relevant.]

g. The 52nd prime number, if 2 is the first, 3 is the second, etc. [239]

a. The arithmetic average of the Roman numerals M, D, C, L, X, V, and I. [238]

b. The positive square root of the ZIP code of Russell, MN [237; ZIP is 56169]

m. Age, to the nearest whole year, of the oldest living Oscar-winning actor or actress (in either a leading or supporting role). [Whatever the answer to this currently is, it must surely be greater than 37 and less than 237, so it falls here.]

e. The two-digit positive integer n that, when its digits are reversed, is equal to 2n – 1. [37]

f. The latitude in degrees North, rounded off to the nearest degree, of the U.S. state capital that has the highest altitude. [36; Santa Fe, NM]

i. Number of different legal moves a player may choose in the starting position in a game of shogi [30: nine possible pawn moves, two lance moves, six rook moves, three king moves, six gold moves, four silver moves]

k. Point value of a cribbage hand consisting of four 5’s and a queen. [28; six different pairs of fives worth 2 points each, and eight different card combinations totaling 15, worth 2 points each, since Q = 10]

d. The fraction of the Earth’s surface that is covered by water. [about .71]

j. If the first four cards dealt to a poker player are the 6, 7, 8, and 9 of hearts, the probability that the player will have a pair or better after being dealt one more card. [9/16; of the 48 cards left in the deck, the player will be helped by the 9 hearts, the 3 5s and 3 10s that aren’t hearts, and the 12 remaining 6s, 7s, 8s, and 9s, for a total of 27 cards; 27/48 = 9/16 = .5625]

n. Probability of throwing an even number on a fair six-sided die if the last 100 throws all were odd. [.5; if the die is fair, it’s a 50-50 chance of throwing an even number regardless of what has happened in the past]

o. Area of Vatican City in square miles. [approximately .172; approximately 110 acres, or 110/640 of a square mile)

h. One percent of the square of 42i, where i = the square root of –1. [–17.64]

c. 0 degrees Fahrenheit, in degrees Celsius [–17 7/9 = –17.7777 etc.]

Results of Online Contest #22
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