# Puzzles

## Archive

Show me a random puzzle**Most recent collections**

#### Sunday Afternoon Maths LXVII

Coloured weightsNot Roman numerals

#### Advent calendar 2018

#### Sunday Afternoon Maths LXVI

Cryptic crossnumber #2#### Sunday Afternoon Maths LXV

Cryptic crossnumber #1Breaking Chocolate

Square and cube endings

List of all puzzles

## Tags

volume geometry factors star numbers triangle numbers planes wordplay complex numbers grids sport speed sums surds rectangles colouring perimeter dodecagons area doubling shapes menace numbers dice chess means lines time crossnumbers squares 3d shapes probability calculus perfect numbers circles symmetry functions addition ellipses remainders pascal's triangle trigonometry unit fractions routes odd numbers graphs rugby sequences people maths coins crosswords games integration irreducible numbers number chocolate shape parabolas clocks sum to infinity folding tube maps algebra 2d shapes hexagons digits cards differentiation partitions christmas mean balancing coordinates percentages factorials advent cube numbers multiples arrows bases scales square numbers money palindromes proportion spheres multiplication prime numbers books averages square roots quadratics ave fractions angles regular shapes floors integers taxicab geometry indices cryptic crossnumbers probabilty division triangles chalkdust crossnumber dates polygons cryptic clues logic## 23 December

Today's number is the area of the largest area rectangle with perimeter 46 and whose sides are all integer length.

## 12 December

There are 2600 different ways to pick three vertices of a regular 26-sided shape. Sometime the three vertices you pick form a right angled triangle.

Today's number is the number of different ways to pick three vertices of a regular 26-sided shape so that the three vertices make a right angled triangle.

## Equal lengths

The picture below shows two copies of the same rectangle with red and blue lines. The blue line visits the midpoint of the opposite side. The lengths shown in red and blue are of equal length.

What is the ratio of the sides of the rectangle?

## Is it equilateral?

Source: Chalkdust issue 07

In the diagram below, \(ABDC\) is a square. Angles \(ACE\) and \(BDE\) are both 75°.

Is triangle \(ABE\) equilateral? Why/why not?

## 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.