mscroggs.co.uk
mscroggs.co.uk

subscribe

Puzzles

What is the sum?

What is \(\displaystyle\frac{1}{\sqrt{1}+\sqrt{2}}+\frac{1}{\sqrt{2}+\sqrt{3}}+...+\frac{1}{\sqrt{15}+\sqrt{16}}\)?

Show answer

19 December

1 = 1/2 + 1/4 + 1/8 + 1/16 + 1/16. This is the sum of 5 unit fractions (the numerators are 1).
In how many different ways can 1 be written as the sum of 5 unit fractions? (the same fractions in a different order are considered the same sum.)

Shooting hoops

Source: Alex Bolton
You spend an afternoon practising throwing a basketball through a hoop.
One hour into the afternoon, you have scored less than 75% of your shots. At the end of the afternoon, you have score more than 75% of your shots.
Is there a point in the afternoon when you had scored exactly 75% of your shots?

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 2023

Advent calendar 2022

Advent calendar 2021

Advent calendar 2020


List of all puzzles

Tags

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

Archive

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