# Puzzles

## Archive

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#### 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

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

Source: Puzzle Critic

Pick a number. Call it \(n\). Write down all the numbers from \(n+1\) to \(2n\) (inclusive). For example, if you picked 7, you would write:

$$8,9,10,11,12,13,14$$
Below each number, write down its largest odd factor. Add these factors up. What is the result? Why?

## Odd squares

Source: Maths Jam

Prove that 1 and 9 are the only square numbers where all the digits are odd.

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