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Homework Statement:
 This is not a homework problem. I was trying to solve a puzzle from a book : 536 curious problems and puzzles. Puzzle no. 199 in the attached picture.
Relevant Equations:

The three terms should look like:
##2 a_1 + d , ~~ 2 a_1 + 2d , ~~ 2a_1 + 3d ##
After trying a few combinations of a1 and d, I looked up the answer and the anwer was: 482, 3362, 6242, where d is 2880.
After seeing such a complicated answer a few questions popped into my head:
1. Could someone have actually manually worked this puzzle out or did the author just ran a simulation to find such unique facts to create a puzzle?
2. Did people in the time before logarithms actually attempt to solve such problems? If yes, how would they go about it?
P.S. I have read a book on Fermat's Last Theorem and know that people did work for years and years on such problems, but would love to get some additional perspective. It would be great if you could refer me to a book or site that discusses such ideas.
Thanks
After seeing such a complicated answer a few questions popped into my head:
1. Could someone have actually manually worked this puzzle out or did the author just ran a simulation to find such unique facts to create a puzzle?
2. Did people in the time before logarithms actually attempt to solve such problems? If yes, how would they go about it?
P.S. I have read a book on Fermat's Last Theorem and know that people did work for years and years on such problems, but would love to get some additional perspective. It would be great if you could refer me to a book or site that discusses such ideas.
Thanks
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