In how many ways, counting ties, can eight horses cross the finishing line?
(For example, two horses, A and B, can finish in three ways: A wins, B wins, A and B tie.)
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In 
ABC, draw AD, where D is the midpoint of BC.
If 
ACB = 30° and ADB = 45°, find ABC.
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A sequence of integers is defined by
Is there a value of p such that the sequence consists entirely of prime numbers?
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If the equation x4 − x3 + x + 1 = 0 has roots a, b, c, d, show that 1/a + 1/b is a root of x6 + 3x5 + 3x4 + x3 − 5x2 − 5x − 2 = 0.
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The minute hand of a clock is twice as long as the hour hand. At what time, between 00:00 and when the hands are next aligned (just after 01:05), is the distance between the tips of the hands increasing at its greatest rate?
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Point P lies inside ABC, and is such that PAC = 18°, PCA = 57°, PAB = 24°, and PBA = 27°.
Show that ABC is isosceles.
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Observe that
Are there any other primes p such that (p − 1)! + 1 is a power of p?
Hint 1 - Hint 2 - Answer - Solution
Find all positive real numbers x such that both 
+ 1/ and 
+ 1/ are integers.
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The towns of Alpha, Beta, and Gamma are equidistant from each other. If a car is three miles from Alpha and four miles from Beta, what is the maximum possible distance of the car from Gamma? Assume the land is flat.
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The smallest distance between any two of six towns is m miles. The largest distance between any two of the towns is M miles. Show that M/m 
. Assume the land is flat.
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