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题目： $$(30^{30}) * (29^{29}) * (28^{28}) * . . . * (3^{3}) * (2^{2}) * (1^{1}) = N$$What is the highest value of K, such that $$\frac{N}{(125^{K})}$$ is an integer?

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题目： This year, a woman has a lucrative one-year position. During this year, she will give a fraction f of her salary to her husband, a private investor, to invest and they will live this year on the remainder. Through investments, her husband can turn each dollar she gives him into 1 + r, which will be deposited in a bank account. Their goal is to save & invest enough money so they can live off this money for two years following the end of the wife's position. Toward this end, they want to choose f such that the amount in the account at the end of the year is twice what they lived off this year. In terms of r, what should f be?

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题目： Pump A can empty a pool in A minutes, and pump B can empty the same pool in B minutes. Pump A begins emptying the pool for 1 minute before pump B joins. Beginning from the time pump A starts, how many minutes will it take to empty the pool?

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题目： Given that $$n = 10^{a} + 10^{b} + 10^{c}$$, where a, b, and c are distinct positive integers, how many different positive values of n result if n is less than 1 billion (1,000,000,000) ?

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题目： In the diagram above, angle C = 90º and AC = BC. Point M is the midpoint of AB. Arc AXB has its center at C, and passes through A and B. Arc AYB has its center at M and passes through A and B. The shaded region between the two arcs is called a "lune." What is the ratio of the area of the lune to the area of triangle ABC?

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题目： In the diagram above, the triangle is equilateral with a side of 2. All three circles are of equal size and all are tangent to each other and to two sides of the triangle. Which of the following is the radius of one of the circles?

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题目： At a certain university, 60% of the professors are women, and 70% of the professors are tenured. If 90% of the professors are women, tenured, or both, then what percent of the men are tenured?

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题目： If points A and B are randomly placed on the circumference of a circle with radius 2, what is the probability that the length of chord AB is greater than 2?

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题目： What is the sum of all possible solutions of the equation$$|x + 4|^{2} - 10|x + 4| = 24?$$

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题目： Fifteen points are evenly spaced on the circumference of a circle. How many combinations of three points can we pick from these 15 that do not form an equilateral triangle?

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题目： In the game of Dubblefud, red chips, blue chips and green chips are each worth 2, 4 and 5 points respectively. In a certain selection of chips, the product of the point values of the chips is 16,000. If the number of blue chips in this selection equals the number of green chips, how many red chips are in the selection?

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题目： How many integers between 1 and$$ 10^{21}$$ are such that the sum of their digits is 2?

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题目： In the coordinate plane, rectangular region R has vertices at (0,0), (0,3), (4,3), and (4,0). If a point in region R is randomly selected, what is the probability that the point's y-coordinate will be greater than its x-coordinate?

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题目： $$({\sqrt{5+\sqrt{5}}-}{\sqrt{5-\sqrt{5}}})^{2}$$=

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题目： In the diagram, ∠L = ∠M = 90°, KL = 4, LM = 8, MN = 10, and JN = JK = 13. What is the area of JKLMN?