Start one of the ropes on fire from both ends and the other one from one end. After a half an hour one rope will be completely burnt and the other will be half burnt. At this point you light the final rope from the unlit side and it will take 15 minutes for the remaining half of the rope to burn, for a total of 45 minutes.

4. Once you grab 4 you will definitely have 2 of the same color.

There is a 50 percent chance.

When the last passenger gets on seats 2 – 99 will be taken for sure. Each of these passengers would take their seats if they were available, so the only seat remaining at the end would be 1 or 100. So there is a 50 percent chance that passenger 100 would get seat 100.

They can start a fire of their own with the matches and the wind will blow that fire in the same direction as the forest fire and they can take refuge in the section of the forest they burn down.

Pour one of the glasses of milk into an empty glass.

7. If you break the batteries into 3 groups: Two groups of 3 and one group of 2. By doing this you guarantee that one of the groups has 2 working batteries. Both of the groups of 3 have 3 possible combinations of 2 batteries and the group of 2 only has 1 combination. So, 3 + 3 + 1 = 7 tries at most to find two working batteries.

Balance.

Switch on two of the light bulbs for a long enough period of time for them to get hot. Then switch off one of those light bulbs and switch on one of the light bulbs that was off. At this point there will be a light bulb that is hot and on, hot and off, cold and on, and cold and off (allowing you to figure out which bulb goes to which switch).

2. The first page in each book is page number 1 regardless of how they are oriented and 1 + 1 = 2.

He can propose a plan that he gets 98 pieces of gold, the 3rd pirate gets 1 piece, and the 5th pirate gets 1 as well.

If there were just 2 pirates the younger pirate would definitely deny the plan so he could get all of the gold.

If there were 3 pirates the first pirate can offer the second pirate 1 piece of gold and take the rest himself because the second pirate wouldn’t get anything if he has to propose a plan himself.

If there were 4 pirates the first pirate could take 99 for himself and offer 1 to the youngest pirate. They would both agree. If the youngest disagrees then he won’t get any gold in the next plan.

So when there are 5 pirates it is in the interest of the 3rd and 5th pirate to accept 1 piece, because if they don’t they won’t get anything in the next plan.