# 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

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

## 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 \(\pi\))?

## 1 December

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

## Cutting corners

Source: New Scientist Enigma 1773

The diagram below shows a triangle \(ABC\). The line \(CE\) is perpendicular to \(AB\) and the line \(AD\) is perpedicular to \(BC\).

The side \(AC\) is 6.5cm long and the lines \(CE\) and \(AD\) are 5.6cm and 6.0cm respectively.

How long are the other two sides of the triangle?

## Quarter circle

Source: Maths Jam

A quarter circle is drawn in a square. A rectangle is drawn in the corner of the square which touches the circle and has sides of length 8 and 1.

What is the length of a side of the square?