Six straight cuts
What is the largest number of pieces a round pizza can be cut into with 6 straight cuts, if the pieces are not moved between cuts?
Fractions, decimals with at least 3 significant digits, and expressions such as sqrt(2)/2, e^-1 or pi/4.
Each new cut adds as many pieces as the number of pieces of pizza it passes through.
The -th cut can cross the earlier cuts at most once each.
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Idea. A new cut is split by the earlier cuts into segments, and each segment divides one piece into two. To get the most pieces, make every cut cross all the earlier ones inside the pizza, at different points.
Step 1. The -th cut crosses at most earlier cuts, so it is split into at most segments and adds at most pieces.
Step 2. Starting from 1 piece, 6 cuts give at most pieces, and cuts in general position (no two parallel, no three through a point, all crossings inside the pizza) reach it.
In general. cuts give at most pieces: 2, 4, 7, 11, 16, 22, ...