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 2023

Advent calendar 2022

Advent calendar 2021

Advent calendar 2020


List of all puzzles

Tags

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

Archive

Show me a random puzzle
▼ show ▼
© Matthew Scroggs 2012–2024