# 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

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