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

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.
These three vertices 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 

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

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

Archive

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