An officer and 269 soldiers in his army detachment are to cross a river. Two boys are rowing about in the river in a small boat. The boat is so small that only one grown man alone can cross the river in it.
How can the 270 soldiers get across the river? And in how many boat crossings? At the end, the two boys should be left together with their boat.
Time to solve: 10 minutes.
Do not jump to an easily available answer. Think logically, think deep.
Solution to the river crossing puzzle for an army detachment in a small boat
Logical reasoning to arrive at the first conclusions
Conclusion 1: If the two boys are always together, the boat won't be available for crossing of any soldier. So, the two boys must be separated.
Conclusion 2: One boy should be on the near shore with the boat and the other on the far shore waiting for a soldier to cross and bring back the boat to the near shore.
The second result is the key to move ahead towards the solution on firmer grounds.
Fact: Only one soldier can get across alone in the boat.
Enough knowledge to plan the crossing of the first soldier
Where would we start? Where would the two boys be with their boat for the first soldier crossing?
Conclusion 3: The boys cannot be on the near shore with their boat for the first soldier crossing—there would be no one on the far shore to bring back the boat.
Conclusion 4: Starting point: The two boys on the far shore with their small boat.
- First crossing: One boy is left alone on the far shore and the second boy rows back to the near shore.
- Second crossing: The first soldier rows alone to the far shore.
- Third crossing: The lone boy waiting on the far shore rows back to the near shore.
- Fourth crossing: The two boys again row across to the far shore. Situation is exactly as at the start.
It took 4 boat crossings for the first soldier to get across.
Plans for the second and 269th soldier to get across the river
In the same way, repeating the four boat crossings of the first soldier, the second soldier gets across in another 4 boat crossings.
And it takes 269 x 4 = 1076 boat crossings for 269 soldiers to gets across the river.
Final crossing of the lone officer
What is the situation after the 269th soldier reached the far shore?
The boy waiting on the far shore would row back to the near shore and along with the second boy cross over again to the far shore creating the situation exactly same as the start. These two crossings are included in the 1076 boat crossings to take 269 soldiers across the river.
Starting status for the last crossing:The lone officer is on the near shore and the two boys with the boat and 269 soldiers are on the far shore.
- First crossing for the final crossing of the officer: One boy rows back alone with the boat to the near shore leaving the other boy on the far shore.
- Second crossing for the final crossing of the officer: The officer rows across alone and joins his forces, but the two boys are not yet together with their boat. One more crossing is needed to fulfill the puzzle conditions.
- Third crossing to complete the successful crossings: The lone boy waiting on the far shore rows back to the near shore and joins the other boy together with their boat.
They need not row together again to the far shore to create the starting situation. All that is needed for them: to be together with their boat.
Solution: 1076 + 3 = 1079 is the total number of boat crossings needed to get all 270 soldiers including their officer to get across the river and leave the two boys together with their boat.
Alert: At first, when you discover the key idea of 4 boat crossings for each soldier, you may hastily form the answer as total boat crossings needed: 4 x 270 = 1080. That will be wrong—the fourth crossing at the end will be superfluous and unnecessary.
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