Miscellaneous
Consider the operation "minus the reciprocal of," defined by a#b = a - b-1. This is ((1#2)#3) - (1#(2#3)).
How much is -7/30?
The number 2.5252525… can be written as a fraction. This is the sum of the numerator and denominator of the fraction when reduced to lowest terms.
How much is 349?
Susie pays for 4 muffins and 3 bananas. Calvin spends twice as much paying for 2 muffins and 16 bananas. A muffin is this many times as expensive as a banana.
A piece of string is cut in two at a point selected at random. This is the probability that the longer piece is at least x times as large as the shorter piece, in terms of x.
How often is 2/(x + 1) of the time?
A 3-4-5 right triangle is inscribed in circle A, and a 5-12-13 right triangle is inscribed in circle B. This is the ratio of the area of circle A to the area of circle B.
How much is 25:169?
Tom has a collection of 13 snakes, 4 of which are purple and 5 of which are happy. He observes that all of his happy snakes can add, none of his purple snakes can subtract, and all of his snakes that can't subtract also can't add.
This is one of the following conclusions that can be drawn about Tom's snakes.
Purple snakes can add.
Purple snakes are happy.
Snakes that can add are purple.
Happy snakes are not purple.
What is "Happy snakes are not purple"?
Let S be the set of the 2005 smallest positive multiples of 4, and let T be the set of the 2005 smallest positive multiples of 6. This is the number of elements common to S and T.
How many are 668 elements?
The common logarithm here is log base 10. log(x - 40) + log(60 - x) < 2 for this many positive integers x.
How many is 18 integers?
Three fair six-sided dice are rolled. This is the probability that the values shown on two of the dice sum to the value shown on the remaining die.
How often is 5/24 of the time?
A square with side length x is inscribed in a right triangle with sides of length 3, 4, and 5 so that one vertex of the square coincides with the right-angle vertex of the triangle. A square with side length y is inscribed in another right triangle with sides of length 3, 4, and 5 so that one side of the square lies on the hypotenuse of the triangle. This is x/y?
How much is 37/35?
Trickster Rabbit agrees with Foolish Fox to double Fox's money every time Fox crosses the bridge by Rabbit's house, as long as Fox pays 40 coins in toll to Rabbit after each crossing. The payment is made after the doubling, Fox is excited about his good fortune until he discovers that all his money is gone after crossing the bridge three times. This is the number of coins Fox had at the beginning.
How many are 35 coins?
This is the number of positive integer divisors of 20042004 that are divisible by exactly 2004 positive integers.
How many are 54 divisors?
L=((16)^(⅕)) * (((16)^(⅕))^(⅕)) * …
This is L.
How much is 2?
Define a good word as a sequence of letters that consists only of the letters A, B, and C—some of these letters may not appear in the sequence—and in which A is never immediately followed by B, B is never immediately followed by C, and C is never immediately followed by A. This is the number of seven-letter good words there are.
How many are 192 good words?
Two different points, C and D, lie on the same side of line AB so that ΔABC and ΔBAD are congruent with AB = 9, BC = AD = 10, and CA = DB = 17. The intersection of these two triangular regions has area m/n, where m and n are relatively prime positive integers. This is m + n.
How much is 59?