Henry Ernest Dudeney/Puzzles and Curious Problems/89 - Forming Whole Numbers

Puzzles and Curious Problems by Henry Ernest Dudeney: $89$

Forming Whole Numbers

Can the reader give the sum of all the whole numbers that can be formed with the four figures $1$, $2$, $3$, $4$?

That is, the addition of all such numbers as $1234$, $1423$, $4312$, etc.

You can, of course, write them all out and make the addition,

but the interest lies in finding a very simple rule for the sum of all the numbers that can be made with $4$ different digits selected in every possible way, but $0$ excluded.

Sources

• 1932: Henry Ernest Dudeney: Puzzles and Curious Problems ... (previous) ... (next): Arithmetical and Algebraical Problems: Digital Puzzles: $89$. -- Forming Whole Numbers
• 1968: Henry Ernest Dudeney: 536 Puzzles & Curious Problems ... (previous) ... (next): Arithmetical and Algebraical Problems: Digital Puzzles: $126$. Forming Whole Numbers