Soldiers and the Tiny Rowboat Puzzle

Yes, all 25 soldiers can cross the river using the two boys and the small boat, and the boys are left with the boat at the end.

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We use the two boys to ferry the boat back and forth so the soldiers can cross one at a time:

1. Both boys cross to far side → 1 trip
2. One boy returns → 1 trip
3. One soldier crosses → 1 trip
4. Other boy returns → 1 trip

Repeat steps 1–4 for each soldier. Each soldier requires 4 trips (two by boys together, two solo returns).

📊 Breakdown of Trips:

• Each soldier crossing takes 4 boat trips.
  • 1 trip: boys go over
  • 1 trip: boy returns
  • 1 trip: soldier goes over
  • 1 trip: other boy returns
• So:
  → 4 trips per soldier × 25 soldiers = 100 trips

BUT we can optimize.

⚡ Optimized Logic:

Let’s define it with fewer total trips by looping cleverly:

1. Both boys go over → 1 trip
2. One boy returns → 1 trip
3. Soldier crosses → 1 trip
4. Other boy returns → 1 trip
   → Repeat this pattern.

So each soldier crossing uses 4 trips, and after 25 soldiers, we have:

• 25 soldiers crossed
• Boys on original side

But after the last soldier, we don't need to return the boy—both boys can stay.

So we remove the last unnecessary return:

✅ Total boat trips:

• (4 × 25) − 2 = 98 boat trips

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