# 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

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

Source: Radio 4's Puzzle for Today (set by Daniel Griller)

Six different (strictly) positive integers are written on the faces of a cube. The sum of the numbers on any two adjacent faces is a multiple of 6.

What is the smallest possible sum of the six numbers?

## Fair dice

Source: Futility Closet

Timothy and Urban are playing a game with two six-sided dice. The dice are unusual: Rather than bearing a number, each face is painted either red or blue.

The two take turns throwing the dice. Timothy wins if the two top faces are the same color, and Urban wins if they're different. Their chances of winning are equal.

The first die has 5 red faces and 1 blue face. What are the colours on the second die?

## Tetrahedral die

When a tetrahedral die is rolled, it will land with a point at the top: there is no upwards face on which the value of the roll can be printed. This is usually solved by printing three numbers on each face and the number which is at the bottom of the face is the value of the roll.

Is it possible to make a tetrahedral die with one number on each face such that the value of the roll can be calculated by adding up the three visible numbers? (the values of the four rolls must be 1, 2, 3 and 4)