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 2019

Sunday Afternoon Maths LXVII

Coloured weights
Not Roman numerals

Advent calendar 2018

Sunday Afternoon Maths LXVI

Cryptic crossnumber #2

List of all puzzles

Tags

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

Archive

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