Question

After solving this problem, include a verbal protocol of how you went about solving each step. A verbal protocol is simply a procedure where you verbalize (or in this case write down) each step as you solve a problem. The verbal protocol should include your thought processes - while you can combine some of the steps to avoid repeating yourself (e.g. "I did step a, b then c, and then repeated those steps for each option until I found the right one"). Feel free to use anything we've discussed about puzzle solving!

Question: River problem with a twist.
four police officers are attempting to chase an escaped criminal across a river. the criminal swam across, but the police gear makes them too heavy to swim themselves. luckily, there's a boat nearby. however, their boat can hold only two people at a time. the first trip across takes one minute, but since the rower gets tired, the second crossing takes two minutes if the same person rows, the third takes three, and so on, getting slower and slower each time the same person rows. in minutes, what's the shortest amount of time if will take the four police officers to get across the river?

Answer 1

The shortest time for four police officers to cross the river, using efficient pairings and accounting for increasing rowing times, totals 15 minutes, pairing the fastest initially and alternating subsequent pairs.

In this river crossing problem with a time twist, four police officers need to shuttle across a river using a boat for two people, with rowing times increasing each trip if the same person rows. To minimize the total time, I paired the fastest officers, A and B, for the initial trips.

First, A and B cross in 1 minute, then one of them rows back in 2 minutes. Next, officers C and D, who haven't crossed, go over in 3 minutes. One returns, taking 4 minutes. Then, A and B cross again, requiring 5 minutes. This process totals 15 minutes for all four officers to reach the other side of the river.

which appears to be the shortest time achievable while ensuring all officers successfully cross. It optimizes pairing the fastest initially, subsequently combining the next fastest pair, and alternating their trips to balance time increases from rowing.