Align the two apples so they're off center to one another. One has 2/3 on the outside to the left, 1/3 to the right, the other 2/3 to the outside to the right, 1/3 to the left.
Bird's eye view, the single line cutting both apples will leave us with the left 2/3 of the first apple and the right 2/3 of the second, and a third portions made of 2 thirds, or another 2/3 of an apple.
One cut, 2 apples, 3 equal portions.
Well, regardless, someone's getting hurt. Have you tried cutting two whole apples, one on top of the other? It's non-trivial! They aren't exactly stable and the rogue's gonna try to swipe one or both as soon as you move your own fingers out of the way. May as well get it over with and stab the rogue to start.
MURDEEER
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The first person decides where the first apple would be cut, such that he would be equally happy with either taking the larger portion or dividing up what remains.
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The second person either says he wants that larger portion, in which case he's done, or he says he wants to divide up what remains, in which case the first person takes the larger portion and is done.
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The third person decides where the second apple would be cut.
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Either the first or second person (depending on the outcome of the second step) picks either the larger portion of the second apple or the two smaller portions.
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The third person takes what remains.
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The two apples are cut and their pieces distributed.
This doesn't guarantee a solution, since it's possible that the third person would have wanted the larger portion of the first apple. It only works if we assume that the first person, when given the motivation to cut fairly, does so with high precision. Otherwise the first person can, by screwing himself over, also screw over the third person.
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The knife is magic, it leaps into the air and Jerry, do a survival roll.
I am fully awake now, and I can't believe I didn't think of cutting it not down the middle. Haha. There's a fairly easy way to calculate where to cut a sphere so that the sphere segment has a desired volume. Similar to the formula used in this video.
Cut one apple in half.
Use integer precision when evaluating equality.
My chaotic neutral undead warlock has the solution.
Cut two 1/6s
