Glad to hear you've been enjoying the game so much! I'm largely very pleased with how the levels and puzzles turned out and it's great to hear that you found the adventure levels compelling.
Regarding this puzzle, I went back to look at it and noticed that it can be particularly tough if you can't figure out where to start from. I suggest starting at the bottom left block, though I think there are other valid starting points. You need to clear a lot of turnips, so I propose that doing a lot of small chains is better than doing fewer, but larger, chains. I think you'll probably have a lot better luck with this info, but if you continue to struggle, feel free to ask for more help.
Also, in case you didn't notice, this is not the only brainteaser on the map - it's just the only one that appears automatically. If you click around at interesting objects and locations, you'll find other puzzles littered about. They're the same ones that are in brainteaser mode, so those who have gone through that mode aren't missing anything, but level 116 and one other easter egg stage are unique to adventure mode. They may not be your cup of tea, but they're there if you want to give them a shot. Just remember that they get harder the closer they are to the end of the map.