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

12 December

These three vertices form a right angled triangle.
There are 2600 different ways to pick three vertices of a regular 26-sided shape. Sometime the three vertices you pick form a right angled triangle.
Today's number is the number of different ways to pick three vertices of a regular 26-sided shape so that the three vertices make a right angled triangle.

 

Show answer

Equal lengths

The picture below shows two copies of the same rectangle with red and blue lines. The blue line visits the midpoint of the opposite side. The lengths shown in red and blue are of equal length.
What is the ratio of the sides of the rectangle?

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

Two semicircles

The diagram shows two semicircles.
\(CD\) is a chord of the larger circle and is parallel to \(AB\). The length of \(CD\) is 8m. What is the area of the shaded region (in terms of \(\pi\))?

Show answer & extension

1 December

What is area of the largest area rectangle which will fit in a circle of radius 10?

Show answer

Cutting corners

The diagram below shows a triangle \(ABC\). The line \(CE\) is perpendicular to \(AB\) and the line \(AD\) is perpedicular to \(BC\).
The side \(AC\) is 6.5cm long and the lines \(CE\) and \(AD\) are 5.6cm and 6.0cm respectively.
How long are the other two sides of the triangle?

Show answer

Quarter circle

Source: Maths Jam
A quarter circle is drawn in a square. A rectangle is drawn in the corner of the square which touches the circle and has sides of length 8 and 1.
What is the length of a side of the square?

Show answer

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

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

Archive

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