# 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

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

## 16 December

There are 204 squares (of any size) in an 8×8 grid of squares. Today's number is the number of rectangles (of any size) in a 2×19 grid of squares

## 14 December

There are 204 squares (of any size) in an 8×8 grid of squares. Today's number is the number of squares in a 13×13 grid of squares

## Squared circle

Each side of a square has a circle drawn on it as diameter. The square is also inscribed in a fifth circle as shown.

Find the ratio of the total area of the shaded crescents to the area
of the square.

## Square deal

Source: Futility Closet

This unit square is divided into four regions by a diagonal and a line that connects a vertex to the midpoint of an opposite side. What are the areas of the four regions?

## Light work

"

*I don't know if you are fond of puzzles, or not. If you are, try this. ... A gentleman (a nobleman let us say, to make it more interesting) had a sitting-room with only one window in it—a square window, 3 feet high and 3 feet wide. Now he had weak eyes, and the window gave too much light, so (don't you like 'so' in a story?) he sent for the builder, and told him to alter it, so as only to give half the light. Only, he was to keep it square—he was to keep it 3 feet high—and he was to keep it 3 feet wide. How did he do it? Remember, he wasn't allowed to use curtains, or shutters, or coloured glass, or anything of that sort.*"## Chessboard squares

It was once claimed that there are 204 squares on a chessboard. Can you justify this claim?

## Equal areas

An equilateral triangle and a square have the same area. What is the ratio of the perimeter of the triangle to the perimeter of the square?