# Puzzles, Issue 04

Solve the puzzles that appeared in Issue 04.

These puzzles appeared in Issue 04 of the magazine.

### 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 $\frac{\text{The sum of the first n odd numbers}}{\text{The sum of the next n odd numbers}}$?

### Two lines

Source: mscroggs.co.uk
Let A and B be two straight lines such that the gradient of A is the y-intercept of B and the y-intercept of A is the gradient of B (the gradient and y-intercept of A are not the same). What are the co-ordinates of the point where the lines meet?

### Odd squares

Source: Maths Jam
How many square numbers are there whose digits are all odd?

The answers to these puzzles are available here.

• ### Read Issue 19 now!

Drinks orders, integer mysteries and the new LMS president feature in our SS24 issue! Plus all your favourite puzzles & columns.
• ### Dear Dirichlet, Issue 19

Game shows, flight and social media bots are among the problems solved in this issue's Dear Dirichlet agony aunt column
• ### Prize crossnumber, Issue 19

Can you solve it?
• ### Which houseplant are you?

Find out by following our simple flowchart
• ### Poetry corner

Thankfully not by Torquil Farquhar de Smith
• ### Top ten: Mathematical norms

The undisputed chart of the best mathematical norms this season