How do you cut a cake into 16 pieces using 5 cuts and no horizontal cuts?

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1176162

2026-03-24 23:20

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I can think of 3 ways to do it but none of them seem especially practicable.

(1) Cut the whole cake in half laterally through the middle as if you were going to fill it with cream. Then cut it right across through the centre 4 times = 16 pieces.

(2) Cut the cake across the middle; make your second cut at right angles to the first through the centre; Bisect those cuts with 2 further cuts each going through the centre. That makes 4 cuts and you now have 8 pieces. Now make a circular cut about 2/3 of the distance between the centre and the perimeter of the cake. To ensure the pieces are equal you'd need to judge carefully the position of this circular cut.

(3) Cut the cake in half; stack one half on top of the other; cut this semicircle in half and stack again, you now have a quadrant equal to a quarter of the cake stacked 4 high and you've made 2 cuts. Cut 3 - cut the quadrant in half; Cut 4 bisect the left hand half of the quadrant; Cut 5 bisect the right hand half of the quadrant - voila - 16 pieces - but I wouldn't try it with a gooey cream cake.

Is there a particular reason that you can't divide it by making 8 cuts in the usual manner?

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