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

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

Archive

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