Puzzle Time

I am always a big fan of brain teaser puzzles. Though I am not a great solver, I love brain teasers. During my childhood, my uncle always gives me brain teasers to solve and I succeed in few as well. Later, I found its nice to solve puzzles to keep your brain sharp. Specially in IT Industries, its very common to get few brain teaser puzzles during your first interview to test your aptitude skills. Here are some puzzles I enjoyed. The first 3 are the ones I had in my first interview and luckily, I solved them all :)

The answers are at the end for your reference. Have fun solving

1. Cut a perfectly cylindrical shaped cake in to 8 equal sized pieces. Remember, you can make only 3 slices.

2. You got 2 candles; each will burn for an hour. You have no markings in the candle to measure it. Now, how will you measure 1.5 hours using just these 2 candles?

3. There is a 20 feet well. A Frog, starting from bottom, jumps 5 feet high and drops down 4 feet. After how many jumps the frog successfully comes out of the well?

4. You have a 3 liter can and a 5 liter can. Also, you got a tank full of surplus water. How will you measure 4 liter of water with just these 2 cans?

5. By moving one of the following digits, make the equation correct. 62 - 63 = 1

6. You have 12 black socks and 12 white socks mixed up in a drawer. You're up very early and it's too dark to tell them apart. What's the smallest number of socks you need to take out (blindly) to be sure of having a matching pair?

7. U2 has a concert that starts in 17 minutes and they must all cross a bridge to get there. All four men begin on the same side of the bridge. You must help them across to the other side. It is night. There is one flashlight. A maximum of two people can cross at one time. Any party who crosses, either 1 or 2 people, must have the flashlight with them. The flashlight must be walked back and forth. It cannot be thrown and other tricks like that are not needed to solve the problem. The solution is simply a matter of allocating resources in a certain order. Each band member walks at a different speed. A pair must walk together at the rate of the slower man's pace: Bono: 1 minute to crossEdge: 2 minutes to crossAdam: 5 minutes to crossLarry: 10 minutes to crossFor example: if Bono and Larry walk across first, 10 minutes have elapsed when they get to the other side of the bridge. If Larry then returns with the flashlight, a total of 20 minutes have passed and you have failed the mission.

8. You are a cook in a remote area with no clocks or other way of keeping time other than a four minute sandglass timer and a seven minute sandglass timer. (The kind you turn over - hourglass shaped) You do have a stove, however, with water in a pot already boiling. Somebody asks you for a nine-minute egg, and you know this person is a perfectionist and will be able to tell if you undercook or overcook the eggs by even a few seconds. What is the least amount of time it will take to prepare the egg? And how will you prepare it so that it is neither undercooked or overcooked?

9. You are standing outside a closed door. On the other side of the door is a room that has three light bulbs in it. The room is completely sealed off from the outside. It has no windows and nothing can get in or out except through the door. On the outside of the room there are three light switches that control each of the respective light bulbs on the other side of the door.Your assignment is to determine which light switch controls which light bulb. You are allowed to enter the room only once, and once you come out, you must be able to state with 100% certainty which light switch controls which light bulb.

10. You are given eight coins and told that one of them is counterfeit. The counterfeit one is slightly heavier than the other seven. Otherwise, the coins look identical. Using a simple balance scale, can you determine which coin is counterfeit using the scale only twice?

Answers:
1. 2 slices on top of the cake to get 4 pieces. Then, make a slice side wards

2. Let the first candle burn to get 1 hour. Now, burn the next candle on both ends.

3. 16 Jumps. On the 16th jump, the frog goes out of the well.

4. Fill the 3-liter can.
Pour the 3 liters of water into the 5-liter can
Fill the 3-liter can again.
Fill up the 5-liter can with the 3-liter can, leaving you with 1 liter left in the 3-liter can.
Empty out the 5-liter can.
Pour the remaining 1 liter of water from the 3-liter can into the 5-liter can.
Fill the 3-liter can.
Pour the 3 liters of water from the 3-liter can into the 5-liter can leaving you with 4 liters of water in the 5-liter can.
5. 2^6 - 63 = 1 (I cant make 6 as power hence used '^' symbol)

6. 3 socks. If the first sock is black, the second one could be black, in which case you have a matching pair. If the second sock is white, the third sock will be either black and match the first sock, or white and match the second sock.

7. Lets take the names as 1,2,5 and 10. First, 1 & 2 goes 2 returns. Next, 5 & 10 goes and 1 returns. Then, 2 & 1 goes together.
8. The answer is 9 minutes. First, flip both hourglasses over and drop the egg into the water. When the four minute timer runs out, flip it again. When the seven minute timer runs out, flip it over. The egg has been cooking seven minutes. Now when the four minute timer runs out again (after eight minutes) flip the seven minute timer back over. Since the seven minute timer has been running only a minute between flips, there's a minute worth of sand left. And when that minute runs out, the egg will have been cooking for exactly nine minutes.
9. Turn one light switch on, wait a few minutes, then turn it off and turn another light switch on. Go into the room and feel the light bulbs. The one that's still warm is connected to the switch that you first turned on, the one that is on was the second switch you turned on, and the last bulb is controlled by the switch that you didn't touch.
10. First weigh three coins against three others. If the weights are equal, weigh the remaining two against each other. The heavier one is the counterfeit. If one of the groups of three is heavier, weigh two of those coins against each other. If one is heavier, it's the counterfeit. If they have equal weight, the third coin is the counterfeit.