FBI Agent Alice is hot on the trail of computer hacker Bob, who is hiding in one of 17 caves. The caves form a linear array, and every night Bob moves from the cave he is in to one of the caves on either side of it. Alice can search two caves each day, with no restrictions on her choice.
For example, if Alice searches (1 2), (2 3), ..., (16 17), then she is certain to catch Bob, though it might take her 16 days.
What is the shortest time in which Alice can be guaranteed of catching Bob?
(In reply to
Puzzle Answer by K Sengupta)
First pass
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DAY 1: Alice checks {2,4}, Bob might be in {1,3} or else 5+. After he moves, he's on {2,4} or 6+.
DAY 2: Alice checks {5,7}. Bob might be in {2,4,6} or else 8+. After he moves, he's in {13,5} or 7+.
DAY 3: Alice checks {8,10}. Bob might be in {1,3,5,7} or 9+. After he moves, he's in {2,4,6,8} or 10+
DAY 4: Alice checks {11,13}. Bob might be in {2,4,6,8,10} or 12+. After he moves, he's in {3, 5, 7, 9, 11} or 13+
DAY 5: Alice checks {14,16}. Bob might be in {1,3,5,7,9,11,13} or 15+. After he moves, he's in {2,4,6,8,10,12} or 14+.
Second Pass
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DAY 6: Alice checks {2,4}. Bob is now in a 6+ even cave. After he moves, he's situated on a 5+ odd cave.
DAY 7: Alice checks {5,7}. Bob is now in a 9+ odd cave. After he moves, he's situated in a 8+ even cave.
DAY 8: Alice checks {8, 10}. Bob is now on a 12+ even cave. After he moves, he's situated In a 11+ odd cave.
DAY 9: Alice checks {11,13}. Bob is now in {15, 17}. After he moves he's situated in {14,16}
DAY 10: Alice checks {14,16} and catches Bob.
Consequently, the minimum amount of time in which Alice can be guaranteed of catching Bob is 10 days.
Edited on July 19, 2022, 8:47 am
Explanation to Puzzle Answer
