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Placing plates

Two players take turns placing identical plates on a square table. The player who is first to be unable to place a plate loses. Which player wins?

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3 December

What is the volume of the smallest cube inside which a rectangular-based pyramid of volume 266 will fit?

2 December

What is the maximum number of lines that can be formed by the intersection of 30 planes?

21 December

This year, I posted instructions for making a dodecahedron and a stellated rhombicuboctahedron.
To get today's number, multiply the number of modules needed to make a dodecahedron by half the number of tube maps used to make a stellated rhombicuboctahedron.

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1 December

What is area of the largest area rectangle which will fit in a circle of radius 10?

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Folding A4 paper

A Piece of A4 paper is folded as shown:
What shape is made?

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Unit octagon

The diagram shows a regular octagon with sides of length 1. The octagon is divided into regions by four diagonals. What is the difference between the area of the hatched region and the area of the region shaded grey?

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Largest triangle

What is the largest area triangle which has one side of length 4cm and one of length 5cm?

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© Matthew Scroggs 2018