mscroggs.co.uk
mscroggs.co.uk

subscribe

Puzzles

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?

3n+1

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

Archive

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

Tags

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

Archive

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