What you may be missing and which hasn’t been specifically spelled out is that the city and the well in question just happened to be on the Tropic of Cancer. On the summer solstice at noon there was no shadow in the well and the blinding sun was reflected straight back at you. The well just happened to be located in a place whose very definition is “the place where the angle of the sun is 0 degrees at noon on the summer solstice”. You don’t need to be measuring simultaneously in 2 places at once because you already have the information for one of the sites.
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I know that you are Using Wit here (as well as making a point 
), but this is just too cool a gif not to share.
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This is so awesome!
I definitely could have made this clearer, the whole calculation depends on this fact so I could have spent more time on it.
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