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The desert expedition

Master playsLevel 4 · Advanced · ●●●●○

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

walk together,
transfer food,
and some may return to base.

Condition: no one can run out of supplies at any time.
What is the minimum number of explorers that must depart to ensure that exactly one completes the crossing?

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Hints

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2 is not enough: after the first useful relief, the companion must return.
With 3 yes: 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).

Solution

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Back to the problem
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:

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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