Diophantus of Alexandria/Arithmetica/Book 1/Problem 17

Problem

 * The sums of $4$ numbers, omitting each of the numbers in turn, are $22$, $24$, $27$ and $20$ respectively

What are the numbers?

Proof
Let $a$, $b$, $c$ and $d$ be the numbers requested.

Then we have:

We use the method of false position.

Set $c = 1$.

Then:

These sums are all $9$ less than what they should be.

So we have to add $3$ to each number, to make: