Problem #14 MEDIUM
The Burning Desert Crossing
Amazon Logic Estimation
Problem Statement
A desert explorer needs to cross a desert that takes exactly 6 days to walk.
The explorer can carry at most 4 days' worth of food and water. He can hire friendly porters to carry supplies for him, but each porter can also carry at most 4 days' worth of supplies for themselves.
What is the minimum number of porters the explorer must hire to successfully cross the desert, assuming everyone must survive and return safely?
Answer & Quick Explanation
Think you've got it? Click below to check your answer.
The explorer needs to hire exactly 2 porters, with one returning on day 1 and the other returning on day 2.
Detailed Editorial Solution
Want to see the step-by-step breakdown? Click below to reveal the editorial.
This is a resource allocation puzzle. We must manage supplies so that the explorer makes it across, while the porters have enough food to walk out and return home safely.
Let's coordinate the journey with 2 porters (Porter A and Porter B):
- **Day 1**: The explorer, Porter A, and Porter B start with 4 days of food each (12 days total).
At the end of Day 1, they have consumed 3 days of food (9 remaining). Porter A gives 1 day of food to the explorer and 1 day to Porter B. Porter A keeps 1 day of food, which is exactly enough to walk back to the start.
*Status at start of Day 2*: Explorer has 4 days, Porter B has 4 days, Porter A is walking home.
- **Day 2**: Explorer and Porter B walk further. At the end of Day 2, they consume 2 days of food (6 remaining). Porter B gives 1 day of food to the explorer. Porter B keeps 2 days of food, which is exactly enough to walk back to the start (2 days away).
*Status at start of Day 3*: Explorer has 4 days of food and is 2 days into the desert.
- **Days 3 to 6**: The explorer walks the remaining 4 days alone, consuming his 4 days of food and arriving safely at the other side.
Everyone survives, and the explorer successfully crosses using only 2 porters.