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 2020

Advent calendar 2019

Sunday Afternoon Maths LXVII

Coloured weights
Not Roman numerals

Advent calendar 2018


List of all puzzles

Tags

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

Archive

Show me a random puzzle
▼ show ▼
© Matthew Scroggs 2012–2021