"Equal" has a slightly different meaning in fair division problems. It doesn't mean "the exact same quantity of matter", so not being able to judge exactly 1/3 of the apple doesn't super matter (though your seed problem can be solved by cutting diagonally through the apples rather than along one side), but rather, that each person gets a portion they value at least as much as the others; maybe some people are willing to take a smaller piece if it means they have no seeds, maybe some people are going to peel their piece so they care more about having the largest internal volume, maybe some people plan to plant the seeds and so they actually value them, maybe some people only care about having the biggest piece.

In practice, for three people this can take as few as 2 cuts or as many as 6; since there's two apples and we can do 2 cuts with one stroke here, there is a fair division solution, but it only works if things go perfectly:

The first person cuts the apples into 3 shares they think are of equal value (perhaps they hate apple cores, so they cut one side off both as above)

The second person points out which share(s) they think are the best

The third person takes the share they consider to be most valuable

The second person takes the share they consider to be most valuable

The first person takes the remaining share, which, since they cut, they must consider equal to the other two.

If the second person doesn't think at least two shares are of equal value, the problem becomes impossible to resolve without more knifeplay.

Yeah. It's a bad question. Why only one stroke? If you cut the apples into cubes and doled them out equally it'd be a much better and more equal experience. The problem presented is a lie, it's just a geometry puzzle.

I’m sure with some calibrating you could just cut off 1/3 of the edible portion. While the core-containing portions would be heavier, the edible apple weight would be the same. It wouldn’t be easy to do first try though

What bothers me is how dangerous that procedure would be

Cut the leaf off with the one slice then each person just eats a third of each apple with their teeth.

Flat skull Winnie the Pooh.tiff

Aim for the jugular

Line the apples up next to each other, I guess. Sort of like taking a single slice through multiple carrots on the cutting board at once. Harder to do with apples given their shape, but I'd the knife is big enough, or you're counting a slice as "single continuous motion" then it is probably valid.

I can't think of any other physical solution that isn't a joke, so this is the most probable puzzle solution. In a D&D setting I might require a slight of hand check with a very low DC to pull off the single slicing motion.

You line up the apple and cut both at the same time

Cut 2/3 of both apples leaving 2x2/3 segments and 2x 1/segments (2/3 cut in half for those of you who struggle with fractions)

Line them up so only 33% of each apple gets cut when you slice.

Stack the apples on top of each other and cut from the top down.