mscroggs.co.uk
mscroggs.co.uk

subscribe

Puzzles

19 December

The diagram below shows three squares and five circles. The four smaller circles are all the same size, and the red square's vertices are the centres of these circles.
The area of the blue square is 14 units. What is the area of the red square?

Show answer

5 December

28 points are spaced equally around the circumference of a circle. There are 3276 ways to pick three of these points. The three picked points can be connected to form a triangle. Today's number is the number of these triangles that are isosceles.

Show answer

2 December

You have 15 sticks of length 1cm, 2cm, ..., 15cm (one of each length). How many triangles can you make by picking three sticks and joining their ends?
Note: Three sticks (eg 1, 2 and 3) lying on top of each other does not count as a triangle.
Note: Rotations and reflections are counted as the same triangle.

Show answer

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

Bending a straw

Two points along a drinking straw are picked at random. The straw is then bent at these points. What is the probability that the two ends meet up to make a triangle?

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

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

Archive

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