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 

Sunday Afternoon Maths LXVII

Coloured weights
Not Roman numerals

Advent calendar 2018

Sunday Afternoon Maths LXVI

Cryptic crossnumber #2

Sunday Afternoon Maths LXV

Cryptic crossnumber #1
Breaking Chocolate
Square and cube endings

List of all puzzles

Tags

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

Archive

Show me a random puzzle
▼ show ▼
© Matthew Scroggs 2019