Henry Ernest Dudeney/Modern Puzzles/49 - Exploring the Desert/Solution

by : $49$

 * Exploring the Desert

Solution

 * $360$ miles out and home.

Working
Let the $9$ men be denoted $A$, $B$, $C$, $D$, $E$, $F$, $G$, $H$ and $J$.

All $9$ men travel $40$ miles into the desert, carrying $9$ gallons each, using the gallon they have in the tank.

$A$ transfers $1$ gallon to each of the other $8$ drivers, and uses his other gallon to get home.

Those $8$ then travel $40$ miles further into the desert on the gallon they have in the tank.

$B$ transfers $1$ gallon to each of the remaining $7$ drivers, and uses his other $2$ gallons to get home.

Those $7$ then travel $40$ miles further into the desert on the gallon they have in the tank.

$C$ transfers $1$ gallon to each of the remaining $6$ drivers, and uses his other $3$ gallons to get home.

Those $6$ then travel $40$ miles further into the desert on the gallon they have in the tank.

$D$ transfers $1$ gallon to each of the remaining $5$ drivers, and uses his other $4$ gallons to get home.

Those $5$ then travel $40$ miles further into the desert on the gallon they have in the tank.

$E$ transfers $1$ gallon to each of the remaining $4$ drivers, and uses his other $5$ gallons to get home.

Those $4$ then travel $40$ miles further into the desert on the gallon they have in the tank.

$F$ transfers $1$ gallon to each of the remaining $3$ drivers, and uses his other $6$ gallons to get home.

Those $3$ then travel $40$ miles further into the desert on the gallon they have in the tank.

$G$ transfers $1$ gallon to each of the remaining $2$ drivers, and uses his other $7$ gallons to get home.

Those $2$ then travel $40$ miles further into the desert on the gallon they have in the tank.

$H$ transfers $1$ gallon to the remaining driver $J$, and uses his other $8$ gallons to get home.

$J$ then travels $40$ miles further into the desert on the gallon he has in the tank.

Then using the $9$ gallons he is carrying, $J$ travels the $9 \times 40 = 360$ miles home.