A desert for six days, provisions for four. Arithmetic seems to prevent the crossing from the beginning. The challenge is to find a way for at least one to get to the other side.
The desert expedition
Riddle statement
Crossing the entire desert requires exactly 6 days of march.
Each explorer can carry provisions for a maximum of 4 days. The 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?
Show solution
Solution
Answer: minimum 3 scouts.
Why 2 is not enough
With a single companion, the best time for relief is at the end of day 1: the companion delivers as much food as possible and returns. But at that point the main explorer can carry a maximum of 4 days of supplies, and still has 5 days of march left. The gap is unbridgeable with just two people.
How it works with 3
- Day 0: P1, P2, P3 leave, each with 4 days of provisions.
- End of day 1: each one has consumed 1 (there are 3 left each). P3 delivers 1 ration to P1 and 1 ration to P2 (P1 = 4, P2 = 4, P3 = 1) and returns — he has just enough left to return.
- End of day 2: P1 and P2 consume 1 (3 and 3 remain). P2 delivers 1 ration to P1 (P1 = 4, P2 = 2) and returns — he has 2 days left to cover the 2 days of return.
- P1 is 4 days from the destination with exactly 4 days of supplies: he arrives right at the other side.
Three explorers are necessary and sufficient.