# Puzzles

## Archive

Show me a random puzzle**Most recent collections**

#### Sunday Afternoon Maths LXVII

Coloured weightsNot Roman numerals

#### Advent calendar 2018

#### Sunday Afternoon Maths LXVI

Cryptic crossnumber #2#### Sunday Afternoon Maths LXV

Cryptic crossnumber #1Breaking Chocolate

Square and cube endings

List of all puzzles

## Tags

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

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

## 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?

## 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 \(\frac{\mathrm{sum\ of\ the\ first\ }n\mathrm{\ odd\ numbers}}{\mathrm{sum\ of\ the\ next\ }n\mathrm{\ odd\ numbers}}\)?