# 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

palindromes regular shapes books doubling quadratics coordinates routes balancing shapes speed number triangle numbers crossnumbers perimeter complex numbers mean integers proportion graphs spheres star numbers circles surds perfect numbers taxicab geometry cube numbers menace probabilty scales wordplay bases clocks rectangles sum to infinity multiplication probability trigonometry division symmetry square roots sequences algebra unit fractions dodecagons folding tube maps triangles colouring people maths time sport chalkdust crossnumber pascal's triangle irreducible numbers lines integration squares square numbers floors 2d shapes dice money prime numbers means advent ave 3d shapes polygons factorials averages rugby planes volume percentages christmas odd numbers shape functions arrows differentiation cryptic clues remainders games fractions parabolas crosswords partitions multiples grids sums dates hexagons area cryptic crossnumbers calculus cards numbers digits chocolate indices coins geometry ellipses addition factors angles chess logic## Not Roman numerals

The letters \(I\), \(V\) and \(X\) each represent a different digit from 1 to 9. If

$$VI\times X=VVV,$$
what are \(I\), \(V\) and \(X\)?

## 24 December

1,0,2,0,1,1

The sequence of six numbers above has two properties:

- Each number is either 0, 1 or 2.
- Each pair of consecutive numbers adds to (strictly) less than 3.

Today's number is the number of sequences of six numbers with these two properties

## 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).

## 21 December

Put the digits 1 to 9 (using each digit exactly once) in the boxes so that the sums are correct. The sums should be read left to right and top to bottom ignoring the usual order of operations. For example, 4+3×2 is 14, not 10. Today's number is the smallest number you can make using the digits in the red boxes.

+ | ÷ | = 2 | |||

× | + | - | |||

× | - | = 31 | |||

+ | + | - | |||

- | × | = 42 | |||

= 37 | = 13 | = -2 |

## 20 December

Today's number is the sum of all the numbers less than 40 that are not factors of 40.

## 17 December

For \(x\) and \(y\) between 1 and 9 (including 1 and 9), I write a number at the co-ordinate \((x,y)\): if \(x\lt y\), I write \(x\); if not,
I write \(y\).

Today's number is the sum of the 81 numbers that I have written.

## 16 December

Arrange the digits 1-9 in a 3×3 square so that the first row makes a triangle number, the second row's digits are all even, the third row's digits are all odd; the first column makes a square number, and the second column makes a cube number.
The number in the third column is today's number.

triangle | |||

all digits even | |||

all digits odd | |||

square | cube | today's number |

## 15 December

Today's number is smallest three digit palindrome whose digits are all non-zero, and that is not divisible by any of its digits.