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

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

Placing plates

Two players take turns placing identical plates on a square table. The player who is first to be unable to place a plate loses. Which player wins?

Show answer & extension

20 December

Earlier this year, I wrote a blog post about different ways to prove Pythagoras' theorem. Today's puzzle uses Pythagoras' theorem.
Start with a line of length 2. Draw a line of length 17 perpendicular to it. Connect the ends to make a right-angled triangle. The length of the hypotenuse of this triangle will be a non-integer.
Draw a line of length 17 perpendicular to the hypotenuse and make another right-angled triangle. Again the new hypotenuse will have a non-integer length. Repeat this until you get a hypotenuse of integer length. What is the length of this hypotenuse?

17 December

The number of degrees in one internal angle of a regular polygon with 360 sides.

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

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

Archive

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