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

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

Archive

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