mscroggs.co.uk
mscroggs.co.uk

subscribe

Sunday Afternoon Maths LVII

 Posted on 2016-11-27 

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

Square factorials

Source: Woody at Maths Jam
Multiply together the first 100 factorials:
$$1!\times2!\times3!\times...\times100!$$
Find a number, \(n\), such that dividing this product by \(n!\) produces a square number.

Show answer & extension

If you enjoyed these puzzles, check out Advent calendar 2024,
puzzles about balancing, or a random puzzle.

Archive

Show me a random puzzle
 Most recent collections 

Advent calendar 2024

Advent calendar 2023

Advent calendar 2022

Advent calendar 2021


List of all puzzles

Tags

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

Archive

Show me a random puzzle
▼ show ▼
© Matthew Scroggs 2012–2025