BrainDen.com - Brain Teasers  # DejMar

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• ### jasen

1. From my reading of the problem, the question can be re-phrased: What is the ratio of the sagitta to the radius of a circle where the apothem is equal to the square-root of half the radius squared?
2. It appears what you (rocdocmac) are saying is: Assume the pizza is a 2-dimensional circle (in a plane of Euclidean space). All cuts are straight lines (i.e., line segments). The confusion that occurs is with the terms vertical and horizontal in the assumed plane, as they imply all vertical cuts are parallel to the imaginary y-axis and all horizontal cuts, if such were allowed, to be parallel to the imaginary x-axis. Yet, as the cuts are given to be in any direction, there was an implied contradiction to that inference.
3. I do believe #3 -- What 3 positive numbers give the same result when multiplied and added together? -- is not grammatically correct. I believe the question should be -- What three positive numbers give the same result when multiplied together and when added together? The adverb should not be implying each operation occurs together, but should occur for each operation as each operation is intended to be independent, yet gives the same result. I do agree with Donald Cartmill that #12 also is not written as it should be.
4. As problems #9 and #14, I admit to having made errors. Problem #12 is one of the problems that can have more than one correct answer. That is, there is more than one way of defining a stroke of a wall clock.
5. Appended post to previous.
6. .
7. A possible solution: