Cutting a cake into 16 pieces with 5 cuts?

Answer 1

All your cuts will be diameters, which means all the cuts will be straight lines that pass through the center of the cake. Your first cut can be anywhere, as long as it's straight and passes through the center. But to make things easy, make your first cut vertical. You now have two equal pieces. Then rotate the cake 90 degrees and make a second diameter cut. It will be perpendicular to the first cut. You now have four equal pieces. Now, rotate the cake 45 degrees and make a third cut through the center. After doing so, rotate the cake 90 degrees from the last cut and make a fourth cut. You should now have eight equal pieces. By now you should be getting the idea. You have to make four more cuts. Each cut should be through the center and should exactly halve the eight slices. This will produce 16 equal slices. By the way, having the interval is a good way of cutting up a square or rectangular cake, too. Every cut should halve the remaining pieces. You start by cutting the cake in half. Then you cut the halves in half. Then you cut the quarters (halves of halves) in half, and so on.

Answer 2

Cut a round cake in eight equal sized wedge shaped pieces with four vertical cuts, then make one horizontal cut through the center of the cake to equal sixteen pieces.

It's slightly more tricky if you are only allowed to cut the horizontal cross-section of the cake (treat the cake as a circle). In this case, first divide the cake with one cut (2 pieces), then cut it again so that it intersects the first cut (4 pieces), then cut it a third time so that it intersects both cuts previously made (7 pieces), then let the fourth cut intersect all three cuts so far (11 pieces), and let the fifth and final cut intersect all four cuts (16 pieces total).

Answer 3

You can cut a cake into 16 pieces with 5 cuts by first making a cross-shaped cut dividing the cake into four equal pieces, then cut each of the four pieces in half horizontally and vertically with the last cut.