# 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

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

## 17 December

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

## Ticking clock

Is there a time of day when the hands of an analogue clock (one with a second hand that moves every second instead of moving continuously) will all be 120° apart?

## Dodexagon

In the diagram, B, A, C, D, E, F, G, H, I, J, K and L are the vertices of a regular dodecagon and B, A, M, N, O and P are the vertices of a regular hexagon.

Show that A, M and E lie on a straight line.

## Three squares

Source: Numberphile

The diagram shows three squares with diagonals drawn on and three angles labelled.

What is the value of \(\alpha+\beta+\gamma\)?