I'm reposting the strategy I used for the earlier puzzles. Sorry if it's confusing; it's the best I could do.
1) Find the puzzles that only take 1 modifier (there should be 5). For the first one, randomly drag the numbered choices on the right over to the modifier box and wait for a result. If you're correct, the message will decode. If you're wrong, you'll get a result. The puzzles are a form of addition {key=ABCD, modifier=EFGH, result=(A+E)(B+F)(C+G)(D+H)}, so if X+Y=Z in any space, it will always = Z. Each symbol is only affected by the ones in the same column (so you don't have to think of them as math at all). So if you got the code wrong, you can look at the last (or first) symbol of the key and target and likely figure out what the missing last symbol of the modifier is (based on the code you've deciphered). Try all the choices that have the correct symbol until you get it right. The same code will work for the other 1-modifier puzzles, so solve them all the same way.
2) For the 2 modifier puzzles (there are also 5), I found it easiest to try two modifiers randomly. I made big boxes for each symbol on a piece of paper. Then I went through my random results and wrote down all the combinations I got for each symbol (for example X: ABB, ACD, DDE). Next, I looked at the last symbol in the key and target and went through the choices one by one. If the first choice had a symbol that would work, I put it in the first box and then tried all the other choices with the final symbol in the second box. If none of those worked, I tried the second choice in the first box with all the matching choices under it (because you already tried it with those above), etc. For example, using the above possibilities for X, if X was the target and A was the key, I'd try all the B's with all the other B's and all the C's with all the D's until I got it right.
3) The 3 modifier puzzles can be solved the same way as the 2's, but they have a lot more possibilities and take longer. I'd recommend using one of the pages with the code to reduce the number of possibilities you need to try.
If none of the above makes sense, you can try the complete brute force method: 1) For the 1 modifier puzzles, try each solution until you get it decoded. 2) Then for the 2 modifier puzzles, put choice 1 in the modifier one box. Then try choices 2-20 (or however many choices there were) in order in modifier two box. If you haven't gotten the solution yet, remove choice 1 from modifier one box and replace it with choice 2, trying choices 3-20 in box two. Continue down the row until it's decoded. 3) For the 3 modifier puzzles, put choice 1 in the modifier one box and choice 2 in the modifier two box. Then try choices 3-20 (or however many choices there were) in order in modifier three box. If you haven't gotten the solution yet, remove choice 2 from modifier two box and replace it with choice 3, trying choices 4-20 in box three. Continue down the row until you've tried all possible combinations with choice 1; then replace choice 1 with choice 2 in box one and proceed down (yes, it's a ton of possibilities).
The petpages tell you which combinations will get the target, so you can only try the choices that might work, eliminating a lot of the choices, especially in stage 3.
I hope this helps people who are having trouble!
Blue graffitied on my signature... But it made me laugh, so it's all good!
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