# Puzzles

## Archive

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#### Advent calendar 2018

#### Sunday Afternoon Maths LXVI

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

Cryptic crossnumber #1Breaking Chocolate

Square and cube endings

#### Sunday Afternoon Maths LXIV

Equal lengthsDigitless factor

Backwards fours

List of all puzzles

## Tags

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