Four friends river crossing puzzle in a 100 kg capacity boat

Submitted by Atanu Chaudhuri on Tue, 02/04/2024 - 01:50

Four friends river crossing with supplies

Four friends Ajoy (90 kg), Biren (80 kg), Chinu (60 kg) and Dipu (40 kg) must cross a river with their supplies (20 kg) in a small boat. The boat can only hold a maximum of 100 kg at a time. How can they cross? Any number of trips back and forth allowed.

Time to find out how they cross in minimum number of trips is 10 minutes.

Find the main difficulties and discover how to get over the difficulties. Same way, use the advantages fully.

Solution to the four friends river crossing puzzle in a boat that can hold 100 kg in a trip

The Challenge: Weight Restrictions

The main difficulty lies in Ajoy's weight. Since he weighs 90 kg and the boat's limit is 100 kg Ajoy can't cross with anyone else (and even with the lightest supplies). This means he needs to make a solo trip, but not first or last (why not?).

Strategies for Success

To solve this puzzle efficiently, let's leverage our advantages:

Dipu's Lightweight Advantage: As the lightest person, Dipu should be involved in many crossings back and forth (the supplies can't row!).
Biren and Supplies: Together, Biren and the supplies weigh exactly 100 kg. To maximize efficiency, Biren should take the supplies across in one trip, but also not on the first trip (why?).
Optimizing Each Trip: We want to maximize the weight carried across the river in each trip and minimize wasted trips. Ideally, the lightest person rows back on return trips.

The Solution: A Step-by-Step Plan

First Crossing & Return: Chinu and Dipu cross together (load exactly 100 kg, maximized efficiency). Dipu stays back on the far side, while Chinu returns with the empty boat. Plan ahead: Dipu waits for Ajoy to arrive on the next trip. He will return with the empty boat.
Second Crossing & Return: Ajoy makes his crucial solo trip across. Dipu returns with the boat, leaving only Ajoy on the far side.
Third Crossing & Return: Biren can't take the supplies yet (who would bring the boat back?). Chinu and Dipu cross second time, with Dipu returning solo. We're planning ahead for Biren's turn: After Biren takes the next trip across with the supplies, Chinu will return with the boat.
Fourth Crossing & Return: As planned, Biren crosses with the supplies (load exactly 100 kg, maximized efficiency). Chinu brings the boat back alone.
Fifth Crossing: Finally, Chinu and Dipu cross together (maximizing load efficiency for the third time), joining their friends and the supplies on the opposite side. They've all successfully crossed the river!

Key Takeaways:

For successful crossing of all four with their supplies in minimum trips, importance of:

Analyzing limitations and leveraging advantages.
Strategic planning of each trip and maximizing weight capacity.
Planning ahead for the next trip.
Putting together the ideas to make the final plan.

Remember: When faced with logic puzzles, take time to identify challenges and leverage any advantages. Planning ahead and thinking a few steps forward can often lead to the most efficient solution.