Logical Puzzle

Solution to December’s Puzzle: Arranging Soldiers in a Row
After some soldiers misbehave, their commander decides to teach them a lesson while testing their powers of logic. He blindfolds them and places hats on their heads. Some hats have a circle on them, and others have a square. He then arranges the soldiers in a column in front of a door and gives them the following orders:

1. Enter the room one by one.
2. After you enter the room, remove your blindfold. Don’t take off your hat or in any way check what sign is on your hat.
3. Line up in a row facing the door. All soldiers who have a circle on their hats should be on the left, and all soldiers who have a square on their hats should be on the right.
4. Don’t communicate with each other verbally or by any other means; rely solely on your sight and logic.
5. If any soldier lines up in the wrong spot, the whole group will face severe penalties.
6. If all soldiers form a row with all circles to the left and all squares to the right, you will get to sleep tonight.
7. Now move!

Assuming you’re one of the soldiers, here’s the logic you would follow after you remove your blindfold and look at the 0, 1, or more soldiers standing in the row in front of you:

• If you enter the room first, simply position yourself somewhere in the room and face the door so that the next soldier can see the sign on your hat.
• If you’re not the first one in the room, look at the soldiers in the row facing the door. If all soldiers in the row have a circle on their hats, go to the right end of the row and face the door.
• If they all have a square on their hats, go to the left end of the row and face the door.
• If some soldiers have a circle (standing to the left) and some have a square (standing to the right), stand between the rightmost soldier who has the circle and the leftmost soldier who has the square.

January’s Puzzle: Crossing the Tunnel
Four people—let’s call them persons A, B, C, and D—need to cross a dark tunnel. Only two people at a time can cross the tunnel, and because the tunnel is very dark, a flashlight is mandatory. Person A can cross the tunnel in 1 minute, person B can cross in 2 minutes, person C can cross in 4 minutes, and person D can make it in 5 minutes. The group has one flashlight, containing batteries that last only 12 minutes. What strategy will enable all members of the group to cross to the other side in 12 minutes before the flashlight’s batteries run down?