mscroggs.co.uk
mscroggs.co.uk

subscribe

Puzzles

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

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

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

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?

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

Two triangles

Source: Maths Jam
The three sides of this triangle have been split into three equal parts and three lines have been added.
What is the area of the smaller blue triangle as a fraction of the area of the original large triangle?

Show answer & extension

Equal side and angle

In the diagram shown, the lengths \(AD = CD\) and the angles \(ABD=CBD\).
Prove that the lengths \(AB=BC\).

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

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

Archive

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