IBM Ponder This #007 · November 1998

You have invited $N$ fussy friends to a party. A square cake has frosting on its top and sides.

How can the cake be cut into $N$ pieces so that every guest receives exactly the same amount of cake and exactly the same amount of frosting?

For a more difficult case, replace the square cake with a $6\times 12$ inch rectangular cake. With $N$ guests, how can the rectangular cake still be divided so that everyone receives equal cake and equal frosting?

Solution

Best opened after a real attempt

Solution

To be added.