mscroggs.co.uk
mscroggs.co.uk

subscribe

Puzzles

Largest odd factors

Pick a number. Call it \(n\). Write down all the numbers from \(n+1\) to \(2n\) (inclusive). For example, if you picked 7, you would write:
$$8,9,10,11,12,13,14$$
Below each number, write down its largest odd factor. Add these factors up. What is the result? Why?

Show answer

Odd squares

Source: Maths Jam
Prove that 1 and 9 are the only square numbers where all the digits are odd.

Show answer & extension

Odd sums

What is \(\frac{1+3}{5+7}\)?
What is \(\frac{1+3+5}{7+9+11}\)?
What is \(\frac{1+3+5+7}{9+11+13+15}\)?
What is \(\frac{1+3+5+7+9}{11+13+15+17+19}\)?
What is \(\frac{\mathrm{sum\ of\ the\ first\ }n\mathrm{\ odd\ numbers}}{\mathrm{sum\ of\ the\ next\ }n\mathrm{\ odd\ numbers}}\)?

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

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

Archive

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