mscroggs.co.uk
mscroggs.co.uk

subscribe

Sunday Afternoon Maths XXI

 Posted on 2014-07-20 

Wool circles

\(n\) people stand in a circle. The first person takes a ball of wool, holds the end and passes the ball to his right, missing a people. Each person who receives the wool holds it and passes the ball on to their right, missing \(a\) people. Once the ball returns to the first person, a different coloured ball of wool is given to someone who isn't holding anything and the process is repeated. This is done until everyone is holding wool. For example, if \(n=10\) and \(a=3\):
In this example, two different coloured balls of wool are needed.
In terms of \(n\) and \(a\), how many different coloured balls of wool are needed?

Show answer & extension

Tags: numbers

Sum equals product

\(3\) and \(1.5\) are a special pair of numbers, as \(3+1.5=4.5\) and \(3\times 1.5=4.5\) so \(3+1.5=3\times 1.5\).
Given a number \(a\), can you find a number \(b\) such that \(a+b=a\times b\)?

Show answer & extension

Tags: numbers
If you enjoyed these puzzles, check out Advent calendar 2023,
puzzles about spheres, or a random puzzle.

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

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

Archive

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