# Puzzles

## Archive

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#### Advent Calendar 2017

#### Sunday Afternoon Maths LXII

What's the Star?#### Sunday Afternoon Maths LXI

XYZ#### Sunday Afternoon Maths LX

Where is Evariste?Bending a Straw

List of All Puzzles

## Tags

time geometry 2d shapes 3d shapes numbers spheres trigonometry complex numbers algebra lines graphs coordinates odd numbers fractions differentiation calculus folding tube maps ellipses triangle numbers money bases triangles squares area square numbers chess probability circles averages speed sport multiples dates factors parabolas functions logic cards games people maths shape prime numbers irreducible numbers probabilty angles proportion dice integration sum to infinity dodecagons hexagons multiplication factorials coins shapes regular shapes colouring grids floors integers rugby crosswords percentages digits sums christmas rectangles clocks menace routes taxicab geometry remainders chalkdust crossnumber palindromes sequences means unit fractions division square roots surds doubling quadratics indices planes volume number partitions ave pascal's triangle mean advent symmetry arrows addition cube numbers star numbers perfect numbers## Bending a Straw

Two points along a drinking straw are picked at random. The straw is then bent at these points. What is the probability that the two ends meet up to make a triangle?

## 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?

## 20 December

Earlier this year, I wrote a blog post about different ways to prove Pythagoras' theorem. Today's puzzle uses Pythagoras' theorem.

Start with a line of length 2. Draw a line of length 17 perpendicular to it. Connect the ends to make a right-angled triangle.
The length of the hypotenuse of this triangle will be a non-integer.

Draw a line of length 17 perpendicular to the hypotenuse and make another right-angled triangle. Again the new hypotenuse will have a non-integer length.
Repeat this until you get a hypotenuse of integer length. What is the length of this hypotenuse?

## 17 December

The number of degrees in one internal angle of a regular polygon with 360 sides.

## 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?

## Cross Diagonal Cover Problem

Source: Gaurish Korpal

Draw with an \(m\times n\) rectangle, split into unit squares. Starting in the top left corner, move at 45° across
the rectangle. When you reach the side, bounce off. Continue until you reach another corner of the rectangle:

How many squares will be coloured in when the process ends?

## Two Semicircles

The diagram shows two semicircles.

\(CD\) is a chord of the larger circle and is parallel to \(AB\). The length of \(CD\) is 8m. What is the area of the shaded region (in terms of \(\pi\))?