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


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


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