In this logic puzzle, you control a UFO that in true 1950s fashion has descended over a field and decided to extract a few lifeforms from the surface of Earth for observation. Each of the sixty challenges gives you an arrangement of fences, cows, and one bull to set up, after which you place a plastic layer that represents the sky over the field, then set your UFO in the starting position:
Your UFO can fly only in orthogonal directions, but you can move anywhere you wish — at least initially. The UFO contains a strong magnet, as does the bull and each cow, and when you fly over an animal, it's lifted in the air and attaches itself to your ship. This is what you want to happen, but two complications hinder your livestock-sucking efforts:
1. The bull — the red token — must be picked up last.
2. The four types of fences are all different heights, which means that sometimes you can't clear a fence if you have one or more cows stuck on your posterior.
More specifically, the red fences have no clearance, so you can pass over them only if you've picked up nothing. The green fences can be cleared by one cow, the white fences two cows, and the yellow fences three cows. With that info now conveyed, in which order must you pick up the cows in the image shown above?
Each challenge has 2-4 cows that must be picked up ahead of the bull, so in challenges with four cows, you must have a clear run to that bull after hoisting the final cow as you can't clear any fences.
After the first forty puzzles, you enter "genius" mode thanks to the introduction of crop circles. When you move one or more cows over a crop circle, you can choose to lift your UFO from the plastic covering device, which will drop those cows onto the circle. You then return your UFO to the plastic sky on a space orthogonally adjacent to that circle and continue moving, with the bull again being the last thing you're allowed to pick up.
These crop circles greatly increase the difficulty of the puzzles given that in the first forty challenges, everything is laid out and nothing changes between when you start moving and when you finish. You can fiddle around with the UFO and solve the puzzle through trial-and-error, restarting as many times as needed, or you can solve it through logic, figuring out the order in which pieces must be picked up, then verifying your reasoning by actually moving the UFO.
Once you hit "genius" mode, however, you open the possibility of cows not being in the same locations over the course of the puzzle, and in the end the cows must always be stacked in the order purple/yellow/orange/blue/red on your UFO, so you need to engage in track-switching to get all the cows in the proper spots so that you can match this line-up when you're exiting the stratosphere and heading back to your own planet.
Invasion of the Cow Snatchers, which I received for review from ThinkFun, effectively has two types of puzzles in the same box, with the first forty puzzles being relatively easy and not that different from one another once you get past, say, puzzle #10, then the final twenty puzzles, which can be become incredibly challenging, especially with four or five crop circles that vastly expand the possible number of moves that you can make.
For more on how this logic puzzle, check out this overview video: