Henry Ernest Dudeney/Puzzles and Curious Problems/110 - An Absolute Skeleton/Solution 1

by : $110$

 * An Absolute Skeleton

Solution
gives this solution:

32418675 312)10114626600     936       ---       754       624       1306       1248       -         582         312         2706         2496         -          2106          1872          -           2340           2184           -            1560            1560

but the following is also a valid solution:

32819764 310)10174126840     930       ---       874       620       2541       2480       -         612         310         3026         2790         -          2368          2170          -           1984           1860           -            1240            1240

declares that:


 * It can soon be discovered that the divisor must be $312$,
 * that $9$ cannot be in the quotient because $9$ times the divisor contains a repeated figure.
 * We therefore know that the quotient contains all the figures $1$ to $8$ once, and the rest is comparatively easy.

But of course his first deduction is not necessarily the case, as we have the possible divisor $310$.