Cube multiples

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?

Show answer & extension

Fair dice

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?

Show answer & extension

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)

Show answer & extension

Tags: dice


Show me a random puzzle
 Most recent collections 

Advent calendar 2019

Sunday Afternoon Maths LXVII

Coloured weights
Not Roman numerals

Advent calendar 2018

Sunday Afternoon Maths LXVI

Cryptic crossnumber #2

List of all puzzles


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


Show me a random puzzle
▼ show ▼
© Matthew Scroggs 2012–2020