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 

Sunday Afternoon Maths LXVII

Coloured weights
Not Roman numerals

Advent calendar 2018

Sunday Afternoon Maths LXVI

Cryptic crossnumber #2

Sunday Afternoon Maths LXV

Cryptic crossnumber #1
Breaking Chocolate
Square and cube endings

List of all puzzles

Tags

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

Archive

Show me a random puzzle
▼ show ▼
© Matthew Scroggs 2019