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


Which is largest, the red or the blue area?

Show answer & extension


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


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


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