I worked on Problem #10 which was the Ahmes' Loaves Sharing problem. I think that it's mind-boggling that the Egyptians used a method of false position to come up with numbers to this hypothetical problem of dividing up 100 loaves of bread between 5 people with 2 complex criteria: the loaf division has to have arithmetic progression and 1/7 of the 3 largest shares must be equal to the 2 smallest shares.
The process of finding the solution to the problem was to reverse engineer the problem by multiplying each share by 100/60 and then adding all the entries together to ensure that they add up to 100. And then taking 1/7 of the largest 3 entry sum and ensuring that they do in fact equal the smallest 2 sum.
As a reflection, this is a pretty interesting exercise that I would not be able to quickly accomplish by doing guess and check. I would definitely need to use algebra to solve the problem efficiently.
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