Q: What is the maximum number of pieces obtained by 13 cuts?

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You would have 8 pieces of cake. A: I can make ten pieces.

If you want an even-sized pieces, you can make a 7-slice pizza. Otherwise, the maximum is 22. (.5x^2 + .5x + 1 is the formula to determine the maximum number of slices if you use "x" cuts.) If you want even-sized slices, you can make a 7-slice pizza. Otherwise, the maximum number of slices is 22. (.5x^2 + .5x + 1 is the formula to determine the maximum number of slices if you use "x" cuts.)

6 if cut like a normal pizza and 3 if cut without overlapping

One horizontal cut, one vertical cut (north-south), one vertical cut (east-west). That will get you 8 pieces.

9 pieces

If no cut intersects any previous cuts, then you can just slice it into 14 pieces.

21 cuts required to cut a cube into 504 identical pieces.

3 mm

7

If you do not re-stack the pieces, then 15 cuts.