mscroggs.co.uk
mscroggs.co.uk

subscribe

Puzzles

19 December

The diagram below shows three squares and five circles. The four smaller circles are all the same size, and the red square's vertices are the centres of these circles.
The area of the blue square is 14 units. What is the area of the red square?

Show answer

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

Archive

Show me a random puzzle
 Most recent collections 

Advent calendar 2019

Sunday Afternoon Maths LXVII

Coloured weights
Not Roman numerals

Advent calendar 2018

Sunday Afternoon Maths LXVI

Cryptic crossnumber #2

List of all puzzles

Tags

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

Archive

Show me a random puzzle
▼ show ▼
© Matthew Scroggs 2012–2020