mscroggs.co.uk
mscroggs.co.uk

subscribe

Puzzles

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

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

Arctan

Prove that \(\arctan(1)+\arctan(2)+\arctan(3)=\pi\).

Show answer & extension

Sine

A sine curve can be created with five people by giving the following instructions to the five people:
A. Stand on the spot.
B. Walk around A in a circle, holding this string to keep you the same distance away.
C. Stay in line with B, staying on this line.
D. Walk in a straight line perpendicular to C's line.
E. Stay in line with C and D. E will trace the path of a sine curve as shown here:
What instructions could you give to five people to trace a cos(ine) curve?
What instructions could you give to five people to trace a tan(gent) curve?

Show answer & extension

arccos + arcsin

What is the value of \(\arccos(x) + \arcsin(x)\)?

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

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

Archive

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