Boltyanski's Cake Problem
V. G. Boltyansky's problem (1977) states: given a cake in the form of a triangle and a box that fits the mirror image of the cake, cut the cake into a minimal number of pieces so that it can be put into the box. The cake has icing on top, so we are not allowed to put it into the box upside down. Examples of cakes that can be cut into two to put into the box are given in this Demonstration. Any cake can be cut into three pieces to put into the box.
Contributed by: Mikhail Skopenkov (March 2011)
(Institute for Information Transmission Problems of the Russian Academy of Sciences, and King Abdullah University of Science and Technology)
Open content licensed under CC BY-NC-SA
V. G. Boltyanski and R. Silverman (trans.), Hilbert's Third Problem, Washington, DC: V. H. Winston & Sons, 1978.
M. Prasolov, M. Skopenkov, and B. Frenkin, "Invariants of Polygons," XIX Summer conference of the International Mathematics Tournament of Towns, 2007.
M. Skopenkov, "Packing a Cake into a Box," arXiv, 2010.