Geometry · Circle · Area comparison · Chords · Symmetry · Fair division
Alenka and Barbara order a pizza. Two straight cuts, perpendicular to each other and neither of them passing through the centre of the pizza, divide it into four pieces. Alenka takes one piece first, then Barbara takes the piece adjacent to it in the clockwise direction, then Alenka takes the next piece clockwise, and Barbara is left with the last one. Which piece should Alenka take first if she wants to end up with more pizza than Barbara?
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Slovenian High School Mathematics Competition for Vega Awards (MaSSA), izbirno (selection) round 2002, 1. letnik, category A, problem 4. Organized by DMFA Slovenije (Society of Mathematicians, Physicists and Astronomers of Slovenia). Source