DejMar

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?

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.

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.

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.

Appended post to previous.

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A possible solution:

Addendum: .

The two moves earlier solution:

Correction to modified solution. (It appears I incorrectly calculated the second leg's length by failing to divide it by 2, and my approximation of the first leg also needed adjusting.)

Modified solution:

The mistaken inference that one might take is that being engaged does not preclude the possibility that the baseball player had previously been married. That another assumption might be needed to be made in order to solve the puzzle.

An apartment and house are different, and clue number 3 does not indicate they are interchangeable, but gives the implication that the house the third basemen and Jones reside contains more than one apartment. Your reference to clue 13 to which it states that Adams lives in a house does not preclude the possibility that Adams may reside in an apartment of an apartment house, not does it state that Adams' sister and Adams lives in the same apartment. From that clue the two siblings could reside in the same or separate apartments -- or in no apartment as the house they reside may, in fact, not be an apartment house, but may be single unit, duplex, or other type of residential house. An assumption that only a non-bachelor could have children contradicts evidence of reality. Yet, in order to find a solution with the givens, it may be one of the assumptions that is needed to be made. Another assumption that might be taken is that one engaged to be married is a bachelor -- even given that the assumption is partially contradicted by clue 15, with divorce being recognized.

Two of the many other possible solutions -- the second of which begins with a 12-letter word, and the first having only the beginning or ending letters being erased, thus not forming words with additional white space within the word.

There are many possible solutions.