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.
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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!
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Problem
Identify, name, and correct the error in the following sentence.
“Before I got on the Subway, I had realized that I had forgotten my wallet,” whined Jon, who was on the verge of tears.
Solution
This is an error of verb agreement. The verb realize does not need the past perfect tense, but rather the perfect. It should read “…I realized that I had forgotten my wallet,…”
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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
This is by far the most complicated problem that has ever been on problem of the week. Feel good if you were able to solve part of it. You likely wont be able to take the solution this far until college Physics. If you have a more intuitive solution, please add it to the comments.
For beginners, you’d do well to recognize that the energy will never be equally distributed between the two pendulums. It will be periodic, with one pendulum having all the energy at certain times and the other having none, and then switched.
For advanced students, the Lagrangian (kinetic energy minus potential energy) is given by:
where
The solution to the problem is then path which minimizes the Lagrangian, or the particular solution to the differential equation:
where q is a generalized coordinate. For anyone who would like an additional challenge, solve this equation and graph some results in MATLAB or your favorite mathematical language. Small angle assumptions may be used. This will be the Problem of the Week this week. Good luck.
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Problem
Choose the best word to complete the following sentence:
The students _____ the food in the cafeteria, saying that it was the best-tasting school lunch in the citiy.
(A) vilified
(B) extolled
(C) squandered
(D) carped
(E) railed at
Solution
The answer is (B) Extolled, which means to lift up or praise highly.
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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
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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.
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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 knows everybody’s percents, etc…).
They draw lots to determine the shooting order. Who has the best chance of survival?
Solution
Even though Corry has only a 50 percent chance of hitting his opponent, he actually has the best chance of surviving, at 50 percent. When drawing lots there are three situations that may arise:
Overall A has a 25% chance of survival, B has a 25% chance, and C has a 50% chance.
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Problem
Identify, name, and correct the error in the following sentence.
Carl, please pick me up from the airport quick so we arrive at the baseball game on time.
Solution
The word quick modifies the verb pick up, so it should be an adverb. The sentence should read “Carl, please pick me up from the airport quickly so we arrive at the baseball game on time.”
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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 x
x x x x
x
Number the rows from top to bottom: 1, 2, 3, and 4. Now take the two outside pennies from row 3 (which has 4 pennies) leaving two, and move them to the outsides of row 1.
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