# Puzzles

## Archive

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#### Sunday Afternoon Maths LXVII

Coloured weightsNot Roman numerals

#### Advent calendar 2018

#### Sunday Afternoon Maths LXVI

Cryptic crossnumber #2#### Sunday Afternoon Maths LXV

Cryptic crossnumber #1Breaking Chocolate

Square and cube endings

List of all puzzles

## Tags

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

Source: New Scientist Enigma 1773

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?

## Equal side and angle

Source: Jim Noble on Twitter

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

Prove that the lengths \(AB=BC\).

## 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?

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**© Matthew Scroggs 2019**