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 2020

Advent calendar 2019

Sunday Afternoon Maths LXVII

Coloured weights
Not Roman numerals

Advent calendar 2018


List of all puzzles

Tags

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

Archive

Show me a random puzzle
▼ show ▼
© Matthew Scroggs 2012–2021