Misprints and Rarities
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#165:No Fault of Mine
Imagine a section of a brick-tiled patio as pictured here:
The individual tiles are 1x2 rectangles. They are placed into a larger rectangular area. Notice what one might call a "fault line" that runs through the pattern: a dividing line that does not cut any of the individual 1x2 tiles, but which separates the whole rectangular area into two smaller rectangles. What is the fewest number of tiles, excluding the trivial case of 1 tile, that may be assembled into a rectangular area so that no fault line exists?
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We are only four days into our journey here on the PRS Exsuscito and a severe disagreement is already underway. Not between the rival horologists, as might be expected (although I suspect that is only a matter of time), but between the horologists and the captain: the ship is heading off course. Captain Harrison refuses to discuss the issue and tersely says that he is "following his orders." What orders? "I cannot help you, Mr. Kennard."
Naturally we are al in a state of uproar. Solitano is demanding that the ship turn around, and Green wants to know the source of the 'orders'. Frankly, I am not overly worried for my safety; Captain Harrison is known to be an upstanding man, and the Exsuscito has an excellent navigator. I am more concerned about what this means for the expedition. Even when it began, I failed to understand why the Academy decided to test different methods of determining longitude by simply throwing all the city's horologists on a single ship, even if their chronometers are not yet finished. With the ship heading to an unknown destination, the expedition is descending into lunacy.
I have tried to spend my time productively, by testing my chronometers and making various measurements on the ship. I surmise that centrifugal forces may affect the counter-oscillating mechanism I employ, but time will tell. I have also been engaged in some interesting discussions with my fellow horologists; not only are they experts in the longitude problem, but I suspect that some of them know more about our ship's 'other' mission than they are revealing.
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