# 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

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