# Puzzles

## Archive

Show me a random puzzle**Most recent collections**

#### 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

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

The picture below shows two copies of the same rectangle with red and blue lines. The blue line visits the midpoint of the opposite side. The lengths shown in red and blue are of equal length.

What is the ratio of the sides of the rectangle?

## 1 December

What is area of the largest area rectangle which will fit in a circle of radius 10?