- A cube of side 4cm is painted with 3 colors red, blue and green in such a way that opposite sides are painted in the same color. This cube is now cut into 64 cubes of equal size.
How many have at least two sides painted in different colors.
How many cubes have only one side painted.
How many cubes have no side painted.
Cubes that have at least two sides painted in different colors are 24 + 8 = 32.
Cubes that have only one side painted are 24.
Cubes that have no side painted = 8.
Cubes that have exactly one side not painted = 0.
- Why is it very common to have a 9 minute snooze interval on alarm clocks, why not 10 instead?
By setting the snooze time to 9 minutes, the alarm clock only needs to watch the last digit of the time. So, if you hit snooze at 6.45, the alarm goes off again when the last digit equals 4. They couldn't make it 10 minutes, otherwise the alarm would go off right away, or it would take more circuitry.
- There are 20 pieces of bread to divide among 20 people. A man eats 3 pieces, woman eats 2 pieces and a child eats half piece of bread. Tell the correct combination of men, women and children so that they are 20 people in total and everyone gets the bread. Note that a man cannot eat less than 3 or more than 3. A woman cannot eat less than 2 or more than 2 and the child cannot eat less than half or more than half piece of the bread. You have to tell there are how may are men, women and children in those 20 people.
There are 5 women, 1 man and 14 children.
- You're riding a horse. To the right of you is a cliff and in front of you is an elephant going the same pace as you and you can't overtake it. To the left of you is a hippo running at the same speed and behind you is a lion chasing you. How do you get to safety?
Get off the merry-go-round.
- The Wisest Son
One day, a father went to his three sons and told them that he would die soon and he needed to decide which one of them to give his property to. He decided to give them all a test. He said, "Go to the market my sons, and purchase something that is large enough to fill my bedroom, but small enough to fit in your pocket. From this I will decide which of you is the wisest and worthy enough to inherit my land."
So they all went to the market and bought something that they thought would fill the room, yet was still small enough that they could fit into their pockets. Each son came back with a different item. The father told his sons to come into his bedroom one at a time and try to fill up his bedroom with whatever they had purchased. The first son came in and put some pieces of cloth that he had bought and laid them end to end across the room, but it barely covered any of the floor. Then the second son came in and laid some hay, that he had purchased, on the floor but there was only enough to cover half of the floor. The third son came in and showed his father what he had purchased and how it could fill the entire room yet still fit into his pocket. The father replied, "You are truly the wisest of all and you shall receive my property." What was it that the son had showed to his father?
The son had showed his father a match. Whenever he lit the match, it filled the entire room with light, yet it was still small enough to fit into his pocket.
- A wise king devised a contest to see who would receive the Princess' hand in marriage. The Princess was put in a 50x50 foot carpeted room. Each of her four suitors were put in one corner of the room with a small box to stand on. The first one to touch the Princess hand would be the winner and become the new King. The rules of the test were that the contestants could not walk over the carpet, cross the plane of the carpet, or hang from anything; nor could they use anything but their body and wits (i.e. no magic or telepathy, nor any items such as ladders, block and tackles etc). One suitor figured out a way and married the Princess and became the new King. What did he do?
Asked the princess to touch his hand.
- You have a fox, a chicken and a sack of grain. You must cross a river with only one of them at a time. If you leave the fox with the chicken he will eat it; if you leave the chicken with the grain he will eat it. How can you get all three across safely?
Take the chicken over first. Go back and bring the grain next, but instead of leaving the chicken with the grain, come back with the chicken. Leave the chicken on the first side and take the fox with you. Leave it on the other side with the grain. Finally, go back over and get the chicken and bring it over.
- You have four chains. Each chain has three links in it. Although it is difficult to cut the links, you wish to make a single loop with all 12 links. What is the fewest number of cuts you must make to accomplish this task?
3 cuts. Cut each link in one chain. Separate them, and use the links to join the ends of the 3 intact chains.
- 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 nor overcooked?
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.
- You are the bus driver. At your first stop, you pick up 29 people. On your second stop, 18 of those 29 people get off, and at the same time 10 new passengers arrive. At your next stop, 3 of those 10 passengers get off, and 13 new passengers come on. On your fourth stop 4 of the remaining 10 passengers get off, 6 of those new 13 passengers get off as well, then 17 new passengers get on. What is the color of the bus driver's eyes?
The eye color of the reader of this problem. The first sentence is the key: "You are the bus driver"