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 

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

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

Archive

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