Monday, March 9, 2015

General Manoeuvres

A platoon of 40 soldiers, inclusive of troopers, senior soldiers, sergeants and commander, was standing by the bank of a river. In order to cross it, they found only a small rubber rowing boat and a pair of paddles, belonging to two young boys. Due to its rather restricted size, the boat can only carry either the two boys together, or a single grown-up.

While the lieutenant - commander of the platoon - was trying to figure out the best way to organize the crossing, the radio received an urgent request: the captain wanted to know exactly how long the platoon would take to cross the river; ie how many minutes, or hours, or days were needed before the last man set his foot on the opposite bank of the river.

The lieutenant worked out that the boat, when carrying the two boys, would take 10 minutes to cross the river. One boy alone on the boat would need 5 minutes. One soldier - soldiers are not the best rowers - would take 8 minutes.

These calculations included the time taken by people to jump on board and get off the boat. After a few seconds, the officer, who had an above average IQ, sent the message with the answer to his captain.

How was the crossing organised, and how long did it take for the entire platoon to cross the river?


General Manoeuvres Puzzle Solution

The manoeuvre was conducted this way:
  1. The two boys cross to the opposite bank (10 mins)
  2. One of them stays there while the other comes back (5 mins)
  3. The boy gets off the boat, a soldier jumps on board and crosses the river (8 mins)
  4. The soldier gets off, and the boat returns with the other boy (5 mins)
This operation required 28 minutes. The sequence had to be repeated as many times as the number of men in the platoon, ie 39 more times. However, it was needed to subtract 5 minutes from from the total: when the last man of the platoon crossed, the time (5 mins) taken by the second boy to cross back must not be counted, as the last soldier had already reached the other bank of the river.

The total time was therefore [(28 * 40) - 5] = 1115 minutes, which amounts to 18 hours and 35 minutes.

Mike Horan points out that it can be done faster if you leave both boys stranded on one side with the boat on the other. The first 39 soldiers cross at 28 minutes each (1092 minutes). You then have the two boys plus the last solider on one side. The final soldier then rows across himself, hence 1092 + 8 = 1100 minutes.