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 2019,
puzzles about people maths, or a random puzzle.


Show me a random puzzle
 Most recent collections 

Advent calendar 2019

Sunday Afternoon Maths LXVII

Coloured weights
Not Roman numerals

Advent calendar 2018

Sunday Afternoon Maths LXVI

Cryptic crossnumber #2

List of all puzzles


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


Show me a random puzzle
▼ show ▼
© Matthew Scroggs 2012–2020