Diophantus of Alexandria/Arithmetica/Book 1/Problem 17/Solution

Problem

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

What are the numbers?

Solution

\(\ds a\)

\(=\)

\(\ds 9\)

\(\ds b\)

\(=\)

\(\ds 7\)

\(\ds c\)

\(=\)

\(\ds 4\)

\(\ds d\)

\(=\)

\(\ds 11\)

Sources

• c. 250: Diophantus of Alexandria: Arithmetica: Book $\text I$: Problem $17$
• 1910: Sir Thomas L. Heath: Diophantus of Alexandria (2nd ed.): The Arithmetica: Book $\text {I}$: $17$
• 1992: David Wells: Curious and Interesting Puzzles ... (previous) ... (next): The First Pure Number Puzzles: $25$