1782 is 3 Times Sum of all 2-Digit Numbers from its Digits

Theorem

$1782$ equals $3$ multiplied by the sum of all the $2$-digit integers that can be formed from its digits.

Proof

The number of $2$-digit integers that can be formed from the digits of $1782$ equals the number of $2$-permutations of $\set {1, 7, 8, 2}$.

That is:

$\set {17, 18, 12, 71, 78, 72, 81, 87, 82, 21, 27, 28}$

Hence:

$17 + 18 + 12 + 71 + 78 + 72 + 81 + 87 + 82 + 21 + 27 + 28 = 594 = \dfrac {1782} 3$

$\blacksquare$

Sources

• 1986: David Wells: Curious and Interesting Numbers ... (previous) ... (next): $1782$
• 1997: David Wells: Curious and Interesting Numbers (2nd ed.) ... (previous) ... (next): $1782$