# Advent calendar 2018

## 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

## Tags

mean means triangles irreducible numbers dates symmetry bases cube numbers sums books multiplication area routes numbers dodecagons averages square numbers circles crosswords 3d shapes grids graphs geometry colouring digits doubling palindromes trigonometry division parabolas taxicab geometry multiples functions factorials partitions clocks time number coins factors cards cryptic clues shape sport addition remainders square roots advent rectangles proportion spheres ellipses chalkdust crossnumber squares balancing sum to infinity scales quadratics integers shapes people maths polygons algebra ave perfect numbers dice hexagons odd numbers menace triangle numbers percentages calculus lines complex numbers probabilty chocolate chess folding tube maps surds pascal's triangle volume sequences coordinates unit fractions floors star numbers wordplay arrows rugby money indices regular shapes fractions prime numbers probability logic angles integration speed 2d shapes differentiation cryptic crossnumbers christmas planes crossnumbers perimeter games## 22 December

In base 2, 1/24 is
0.0000101010101010101010101010...

In base 3, 1/24 is
0.0010101010101010101010101010...

In base 4, 1/24 is
0.0022222222222222222222222222...

In base 5, 1/24 is
0.0101010101010101010101010101...

In base 6, 1/24 is
0.013.

Therefore base 6 is the lowest base in which 1/24 has a finite number of digits.

Today's number is the smallest base in which 1/10890 has a finite number of digits.

Note: 1/24 always represents 1 divided by twenty-four (ie the 24 is written in decimal).