mscroggs.co.uk
mscroggs.co.uk

subscribe

Puzzles

Archive

Show me a random puzzle
 Most recent collections 

Tags

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

Archive

Show me a random puzzle
▼ show ▼

Is it equilateral?

In the diagram below, \(ABDC\) is a square. Angles \(ACE\) and \(BDE\) are both 75°.
Is triangle \(ABE\) equilateral? Why/why not?

Show answer

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.

Show answer

Square deal

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?

Show answer & extension

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."

Show answer & extension

Chessboard squares

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

Show answer & extension

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?

Show answer & extension

© Matthew Scroggs 2019