Puzzle – Death in a Desert

The explorer, “combat archaeologist” and looter of tombs, Dr. Flynn, was trekking across the desert in search of King Solomon’s Mines. Unfortunately for him, the water container in the back of his Land Rover had started leaking. In the first hour, it lost half the number of liters it held plus one liter. In the second hour, it lost half of the remainder plus one liter. In the third hour, it lost half of the remainder again, plus one liter more. In the fourth hour, it lost half the remainder plus one liter more. Now it was completely empty. How many liters did the container hold to start with?

Death in a desert

Solution: Thirty liters. The way to solve it is to work backward — to get zero after the fourth hour it must have lost one plus one more. So in the third hour, it must have lost half of six, plus one more to leave two, and so on.

Illustration for leakage at each hour:

• At 4th hour -> 1 + 1 = 2 lts
• At 3rd hour -> 3 + 1 = 4 lts
• At 2nd hour -> 7 + 1 = 8 lts
• At 1st hour -> 15 + 1 = 16 lts
• Total -> 30 lts.