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Wednesday, July 23, 2008

Birthday Cake

The birthday cake on the picture must be cut into eight equally sized pieces. However, you are allowed to make only 3 straight cuts.

The Question: How can the cake be cut into eight pieces with only 3 straight cuts?

Answer: There is only one solution which solves the problem with three straight cuts, and leaves exactly eight equally shaped portions. One should cut the cake two times vertically in a '+' shape across the top and make the third cut horizontally in the middle of the cake (looking at the cake from the front), as shown in the figure on the right. The disadvantage of this solution is however that only four portions will contain fruit-decoration etc., whereas the other four portions will only contain bottom parts of the cake...

This is how the cake could be cut (seen from above), if we would prefer to have both top and bottom parts in each piece:

Note however that this is not a real solution, since it has non-straight cuts. In this way, we could think of many other 'solutions', like:

Finally, an alternative solution that requires some rearrangement of the pieces after the first two cuts, is the following: like before, make the first two cuts cross-wise, then arrange all four pieces in a row, and make the third straight cut like this:

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