mscroggs.co.uk
mscroggs.co.uk

subscribe

Puzzles

23 December

Today's number is the area of the largest area rectangle with perimeter 46 and whose sides are all integer length.

Show answer

2 December

Today's number is the area of the largest dodecagon that it's possible to fit inside a circle with area \(\displaystyle\frac{172\pi}3\).

Show answer

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

Two triangles

Source: Maths Jam
The three sides of this triangle have been split into three equal parts and three lines have been added.
What is the area of the smaller blue triangle as a fraction of the area of the original large triangle?

Show answer & extension

Overlapping triangles

Four congruent triangles are drawn in a square.
The total area which the triangles overlap (red) is equal to the area they don't cover (blue). What proportion of the area of the large square does each (purple) triangle take up?

Show answer & extension

Unit octagon

The diagram shows a regular octagon with sides of length 1. The octagon is divided into regions by four diagonals. What is the difference between the area of the hatched region and the area of the region shaded grey?

Show answer & extension

Largest triangle

What is the largest area triangle which has one side of length 4cm and one of length 5cm?

Show answer & extension

Circles

Which is largest, the red or the blue area?

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

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

Archive

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