Archive for Math

Thanksgiving Turkeys

Math on November 9th, 2009 Comments Off

Problem You have five Turkeys. If you weigh them in every possible combination of 2, the weights are 16, 18, 19, 20, 21, 22, 23, 24, 26, and 27 kg. What are the individual weights? Solution Come back next week for the solution. If you have a tricky or interesting problem that you’d like to [...]

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SAT Vocabulary

Math on November 8th, 2009 Comments Off

Problem Odysseus was the most _____ of all Greek Kings. Many tales tell of how his cunning won the day. (a) primeval (b) fastidious (c) archetypal (d) adroit (e) punctual Solution Come back next week for the solution! If you have a tricky or interesting problem that you’d like to see on Problem Of The [...]

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Interconnected Pendulums

Math on October 20th, 2009 Comments Off

Problem The bobs of two pendulums are connected by a spring. When one is moved by an angle (theta) theta and released, what is the resulting motion? Do they eventually have the same energy? For physics students, let the pendulums length=L, point mass=M, and spring constant=K. Find the equations of motion for both pendulums. Solution [...]

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Missing Numbers

Math on October 12th, 2009 Comments Off

Problem Solve this simple arithmetic by replacing each # sign with a different digit, 1-9, using each digit only once. ## represents a two-digit number. ## x # —– ## + ## = ## Solution When filled in correctly, the equation is: 17 x 4 —– 68 + 25 = 93 If you have a [...]

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SAT English- Grammar

Math on October 9th, 2009 Comments Off

Problem Find, name, and correct the error in the sentence below: Everyone has their own idea about parenting; it’s a hot topic. Solution This sentence has a pronoun error. Everyone is a singular subject, thus the pronoun their should be his or her. If you have a tricky or interesting problem that you’d like to [...]

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Triple Duel

Math on October 5th, 2009 Comments Off

Problem Three Cowboys Arden, Begley, and Corry compete in a duel. Arden and Begley are both sure shots (they hit their targets 100 percent of the time) while Corry only hits his target 50% of the time. Everybody has perfect knowledge (knows everybody’s percents, knows that everbody knows everybody’s pecents, knows everybody knows that everybody [...]

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Penny Problem

Math on September 28th, 2009 Comments Off

Problem You are given ten pennies arranged like this picture. Move three of them so that the arrow in the opposite direction. Solution Take the top penny and move it to a new row, in the center, under the bottom row into the following configuration: x       x x        x       [...]

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Related Rates

Math on September 21st, 2009 Comments Off

Problem While this problem looks straight from a differential calculus textbook, it requires no advanced math. Two bugs sit on either side of a bubble. The radius r of the bubble is expanding with dr/dt=3 cm/s. The distance between the bugs is d and they sit on either side of a 60 degree arc, find [...]

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Balance Problem

Math on September 15th, 2009 Comments Off

Problem You are given 10 balls, which are all identical. One ball is either heavier or lighter than the rest. Using a balance three times, can you determine which ball is different, and whether the weight is heavier or lighter? This requires no advanced math or tricky way of using the balance. Think it’s too [...]

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Interesting Geometry

Math on September 10th, 2009 Comments Off

Problem I heard this former Putnam problem from a friend. The solution requires no advanced math, just clever thinking. Given a sphere with five points placed at random on its surface. How many points can you guarantee will fall within a well-chosen closed hemisphere? Solution The answer is four. One great circle, which defines the [...]