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.

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