23 December

This number is a prime number. If you treble it and add 16, the result is also prime. Repeating this will give 11 prime numbers in total (including the number itself).

14 December

What is the only palindromic three digit prime number which is also palindromic when written in binary?


Let \(S=\{3n+1:n\in\mathbb{N}\}\) be the set of numbers one more than a multiple of three.
(i) Show that \(S\) is closed under multiplication.
ie. Show that if \(a,b\in S\) then \(a\times b\in S\).
Let \(p\in S\) be irreducible if \(p\not=1\) and the only factors of \(p\) in \(S\) are \(1\) and \(p\). (This is equivalent to the most commonly given definition of prime.)
(ii) Can each number in \(S\) be uniquely factorised into irreducibles?

Show answer & extension


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


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


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