Originally Posted by

**Soroban** Hi, janvdl!

Of course, such a rule would be *messier* than the 11-rule.

Let multiply $\displaystyle abcde$ by 17 and see what happens.

. . . $\displaystyle \begin{array}{ccccccc} & a & b & c & d & e \\

& & & & 1 & 7 \\ \hline

& 7A & 7b & 7c & 7d & 7e \\

a & b & c & d & e \\ \hline

& 7a & 7b & 7c & 7d & 7e \\

+a & +b & +c & +d & +e

\end{array}$

The digits are: .$\displaystyle [a]\;\;[7a+b]\;\;[7b+c]\;\;[7c+d]\;\;[7d+e]\;\;[7e] $

. . with the appropriate "carry" performed.

The basic step seems to be: "Starting at the right, multiply each digit by 7

. . and add the preceding digit (and carry)."

Example: .$\displaystyle 234 \times 17$

Append a zero (0) to both ends: .$\displaystyle 0\,2\,3\,4\,0$

. . $\displaystyle \begin{array}{ccccc}0 & 2 & 3 & 4 & \quad0\\

\downarrow & \downarrow & \downarrow & \downarrow \\

7(0)+2 & 7(2)+3 & 7(3) + 4 & 7(4) + 0 \\

\downarrow & \downarrow & \downarrow & \downarrow \\

2 & ^17 & ^25 & ^28 \\

\downarrow & \downarrow & \downarrow & \downarrow \\

3 & 9 & 7 & 8

\end{array}$

Therefore: .$\displaystyle 234 \times 17 \;=\;3978$