Hence my careful specification that you're multiplying the numbers, not the piles.

I found the use of multiplication particularly useful, since it forced the reader to pay attention to the physical/logical distinction. If, say, addition had been used, then a determined reader could try to use physical constraints alone (though they would be cheating).

If we assume that the 5 apples are spherical, and we cut the largest square sections possible out of each of them (leaving the top and bottom alone, as that doesn't affect whether the shape is a square when viewed from the top down), it turns out that these new squared apples have a volume of about 0.77 times that of a spherical apple. That means that your 2 round apples and your 3 round apples become about 6.49 squared apples. Rounding down, that is, in fact, 6 square apples.

But I do think the illegal operation was kind of the point. It shows that not all mathematical operations can be strictly reduced to physical objects (well, outside of the substrate that's doing the computing, obviously).

Edit: it was