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 floors, 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

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

Archive

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