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The desert expedition

The best thing about The Desert Expedition is that it seems to go one way and resolves another. That little twist is what turns a correct problem into a memorable puzzle.

Crossing the entire desert requires exactly 6 days of walking. Each explorer can carry supplies for a maximum of 4 days.

Explorers can walk together, exchange supplies, and return if they want. How many explorers are needed at least for at least one to reach the other side?

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Hints

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A single explorer is not enough, and neither are two: the problem is creating deposits and still having people able to return.
Think of auxiliary scouts who accompany part of the journey, deliver food and return.
The bottleneck appears at the long halfway point of the journey: you have to get there with someone who can still get back.

Solution

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Answer: minimum 3 explorers. 2 is not enough: - after the first useful relief, the companion must return,

the main explorer cannot accumulate enough supplies to cover 6 full days. With 3 yes: 1. Day 0: P1, P2, P3 leave with 4 days each.

End of day 1: each one has 3. P3 delivers 1 day to P1 and 1 day to P2 (P1=4, P2=4, P3=1) and returns to base (consumes that 1).
End of day 2: P1 and P2 consume 1 (3 and 3 remain). P2 delivers 1 to P1 (P1=4, P2=2) and returns 2 days to base.
P1 is 4 days from the destination with 4 days of food: he arrives exactly. Therefore, 3 is sufficient and 2 is impossible.

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