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:
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


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


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


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