ArchiveShow me a random puzzle
Most recent collections
Sunday Afternoon Maths LXVIIColoured weights
Not Roman numerals
Advent calendar 2018
Sunday Afternoon Maths LXVICryptic crossnumber #2
Sunday Afternoon Maths LXVCryptic crossnumber #1
Square and cube endings
List of all puzzles
Tagsclocks surds square numbers perimeter multiples triangles routes remainders sport integers number indices proportion cube numbers sequences spheres partitions taxicab geometry squares integration wordplay dice probabilty cards averages people maths ave division christmas triangle numbers algebra rugby books percentages coordinates folding tube maps angles mean time probability parabolas star numbers sum to infinity volume polygons differentiation money geometry chess multiplication lines means balancing perfect numbers quadratics area addition calculus colouring factors cryptic crossnumbers digits irreducible numbers scales advent functions speed prime numbers sums dodecagons 3d shapes chocolate complex numbers bases numbers fractions pascal's triangle circles palindromes chalkdust crossnumber square roots ellipses unit fractions doubling factorials coins shape symmetry grids games crossnumbers graphs 2d shapes odd numbers trigonometry menace floors arrows shapes regular shapes crosswords cryptic clues dates planes hexagons rectangles logic
Sunday Afternoon Maths LXIII
Posted on 2018-04-22
Is it equilateral?
Source: Chalkdust issue 07
In the diagram below, \(ABDC\) is a square. Angles \(ACE\) and \(BDE\) are both 75°.
Is triangle \(ABE\) equilateral? Why/why not?
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?