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 2023

Advent calendar 2022

Advent calendar 2021

Advent calendar 2020


List of all puzzles

Tags

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

Archive

Show me a random puzzle
▼ show ▼
© Matthew Scroggs 2012–2024