Difficulty Popularity Aamir has a cube with 4 inch side. On the opposing faces, he uses red, green, and black paint. After that, he cuts it into one inch cubes. Respond to questions (1-4) in relation to the once-inch cubes. Q1. With only one face painted, how many cubes are left? a) 8 b) 16 c) 24 d) 32 Q2 Which number of cubes has two painted faces: a) 8 b) 16 c) 24 d) 32 Q3 Four faces are painted on how many cubes? a) 0 b) 4 c) 8 d) 12 Q4 A) 0 B) 4 C) 8 D) 12 How many cubes are left without any faces painted?
You must be a detective and identify the thief in the puzzle below. How difficult is it?
The detector is fastened to the back of the woman’s blouse as she sits in the chair.
Popularity Difficulty There are five pineapple candies, three strawberry candies, and two mango candies in a closed jar. You cant see inside the jar. How many toffees from the jar do you need to remove in order to have one of each flavor?
9 Explanation: 2 3 5 To determine the necessary number of candies, substitute one for the lowest number (i e. add all the higher numbers (i.e., take one mango candy) e. three strawberry and five pineapple candies) to it. Number of balls needed: 1 + 3 + 5 = 9
Popularity Difficulty After the biggest theft the town had ever seen, a thief fled from the police. In one of the circle-shaped caves’ thirteen chambers, he set up guard. The thief either stays in the same cave or moves to the nearby cave each day. Every day, two police officers go there and have enough time to enter two of the caves. What is the minimum number of days that the cop must catch the thief in, and how will he ensure that it happens?
Every day, one of the officers will rotate clockwise, and the other will rotate counterclockwise. They will catch the thief in this way in no more than seven days.
Difficulty Popularity The world is facing a serious viral infection. Every citizen of various nations has received two bottles from their governments. You as well have been given the same. Now, one pill from each bottle must be taken daily for a month in order to develop a virus immunity. The issue is that you will suffer a painful death if you take just one or two from the same bottle. You quickly open the bottles while using it and pour the tablets into your hand. When three tablets land in your hand, you notice they are identical in appearance and possess the same qualities. Because there are only so many pills you can make, you can’t put them back or you might put the wrong one in and end up dying someday. How will you make sure you are taking the correct medication?
Before using, the tablets must be marked with the letters A and B. In that case, combining the tablets will result in 3A, 2A 1B, 1A 2B, or 3B. You can take one from a different bottle if they are from the same bottles and save the other two for another day. If you draw two from the same bottle and one from another, you will have two pairs of cookies that you can either eat or save.
Difficulty Popularity There are three bags. The first bag has two blue rocks. The second bag has two red rocks. The third bag has a blue and a red rock. All bags are labeled but all labels are wrong. You may open one bag, select one rock at random, observe its color, and then reseal the bag without revealing the color of the remaining rocks. How many of these processes are required to label the bags properly?
Just one example: If you receive Blue Rock with the label “blue+red,” it will be red because all other labels are incorrect. In this way u can logically solve this puzzle.
Popularity Difficulty A set of scales and 12 marbles are given to you. The scales are of the old balance variety. That is, a rod that is balanced in the middle has a small dish hanging from each end of it. The tool allows you to determine whether the contents of the two dishes weigh the same amount or whether the dish with the heavier contents is the one that is lower. The 12 marbles appear to be identical. Actually, 11 of them are the same, and the 12th is heavier than the others. You must locate the unusual marble and throw it away. If you wish, you may use the scales three times, but not more. A special marble may be heavier or lighter than the others, so keep that in mind. You’re expected to recognize it and decide whether it’s heavy or light.
Let’s number the coins from 1 to 12 so that the following scheme can be carried out. Let’s place coins 1, 2, 3, 4 on the left pan and 5, 6, 7, 8, on the right pan for the initial weighing. There are two possibilities. Either they balance, or they dont. If they are in balance, the additional coin belongs to the group 9, 10, 11, or 12. Our second option is to weigh the numbers 9, 10, and 11 against the numbers 1, 2, and 3 (1). If they balance, you will know that the number 12 is a different coin, and you can simply weigh it in comparison to any other coin to determine its weight. (2) 9,10,11 is heavy. You are aware that the alternate coin is a heavy 9, 10, or 11 in this situation. Just compare 9 and 10, and if they balance, 11 is the heavier coin. If not, the heavier one is the heavy coin. (3) 9,10,11 is light. Continue as in the preceding step, but look for the light coin instead. That was the easy part. If the first coin, which should weigh 1, 2, 3, and weighs 5, 6, 7, and 8, does not balance, then any of these coins could be a different coin. We must now keep track of which side is heavier for each of the upcoming weighings in order to move on. Suppose that 5,6,7,8 is the heavy side. We now weigh 1,5,6 against 2,7,8. If they are equal, the other coin is either a 3 or a 4. Weigh 4 against 9, a known good coin. The alternate coin is 3, if they balance, otherwise it is 4. We can determine the weight of the offending coin based on the direction of the tilts. Now, if the ratio of 1,5,6, and 2,7,8, where 2,7,8, is the heavy side, does not balance, either 7 or 8 would be a different, heavy coin, or 1 would be a different, light coin. For the third weighing, weigh 7 against 8. Whichever side is heavy is the different coin. If they balance, then 1 is the different coin. If weighing 1, 5, and 6 versus 2, 7, and 8 reveals that 1, 5, and 6 are on the heavier side, then either 5 or 6 is a different heavy coin or 2 is a different light coin. Weigh 5 against 6. The heavier one is the different coin. If they balance, then 2 is a different light coin.
If you lived in Dubai and had an endless supply of oil along with a 5 liter and a 3 liter jar, how would you measure exactly 4 liters (of course in the fewest possible steps)?
1. Fill 5 liters jar ( 5l-jar:5, 3l-jar:0) 2. Transfer to 3 liters pail (5l-jar:2, 3l-jar:3) 3. Empty 3 liters jar ( 5l-jar:2, 3l-jar:0) 4. Transfer 2q (5l-jar:0, 3l-jar:2) from a 5 to a 3 pail. Fill 5 liters pail(5l-jar:5, 3l-jar:2) 6. Transfer 1q from 5 pail to 3 pail(5l-jar:4, 3l-jar:3).
Popularity Let’s say a table tennis competition had knockout rules, which meant that the loser of the match was eliminated from the competition. 100 players took part in that tournament. How many matches were played?.
99 matches. In a knockout tournament, the total number of matches will always be one fewer than the total number of participants. You may calculate it in any manner. Thus 99 matches were played.
Popularity A peculiar tradition is practiced in a traditional and undeveloped village. Every year, the village chief collects taxes from all of the male residents. But what’s interesting is how taxes are collected. Every male should pay an equal amount of pounds in taxes in the form of grains based on his age. In plainer terms, a man of age 10 will be required to pay 10 pounds of grains, and a man of age 20 will be required to pay 20 pounds of grains. On a riser with seven different weights, the chief is positioned next to a sizable two-pan scale. The chief can only weigh using three of the seven weights according to the intriguing tradition. Can you determine the weights of the seven weights in this situation and the oldest man the chief can measure using those weights?
Before you begin calculating using any method, keep in mind that weights can be placed on both pans. Therefore, the weights are 1, 3, 7, 12, 43, 76, and 102. A 122-year-old man can be weighed using these weights.
Difficulty Popularity Use exactly three matchsticks to divide the area in the image below into two equal parts. Can you do it?.
Rubik’s Cube: A question, waiting to be answered
2 Answers 2
Sorted by:
Given that there are six faces to a cube and each face has $10 times 10 “sides,” the obvious solution would be $6 times 10 times 10 times 10 dollars, or 600 dollars.
But if this is one of those ridiculous “lateral thinking” questions, maybe the paint seeps between the “cracks” and actually covers every “side” of each of the $10 x 10 x 10 = 1000 $ “minicubes” that make up a Rubiks cube, leaving $6000 $ “sides” painted black.
The real question might have been: How many “cubies” have AT LEAST one side painted black if you drop a $10 x 10 x 10 dollar cube into a bucket of the color?
In this instance, there is an untouched $8 times 8 times 8 dollar cube in the middle. So the answer is $10^3 – 8^3 = 488$.
Thanks for contributing an answer to Mathematics Stack Exchange!
Use MathJax to format equations. MathJax reference.
To learn more, see our tips on writing great answers. Draft saved Draft discarded.
Q: Picture a 10x10x10 “macro-cube” on the table. This big cube is made up of 1x1x1 “micro-cubes”. When your dog approaches, he drags the macro cube off the table with his tail, sending it crashing to the floor. The impact causes the entire top layer of microcubes to come off when it collides. How many micro-cubes are on the floor?.
Concentrating on the problem’s structure is the better course of action. The original macro-cube and new smaller macro-cube hold the answer. The number of micro-cubes that fell off determines the difference in their volumes. The volume of a cube is n cubed. The answer is, therefore, 10 cubed – 8 cubed. So, 1,000 – 512 = 488.
Note: A common blunder is for people to believe that the answer is 10 cubed – 9 cubed because only one layer fell off.
Although you probably won’t be given a Rubik’s Cube to solve during your hedge fund job interview, you should be ready to solve a puzzle of some sort. Make sure you think through the question before jumping into an answer. And, for goodness’ sake, answer the question that is asked! Nothing decreases your chance of getting a job you are qualified to do faster than not answering the right question.
Special thanks for this interview question to Timothy Crack, author of Heard on the Street: Quantitative Questions from Wall Street Job Interviews
Let’s number the coins from 1 to 12 so that the following scheme can be carried out. Let’s place coins 1, 2, 3, 4 on the left pan and 5, 6, 7, 8, on the right pan for the initial weighing. There are two possibilities. Either they balance, or they dont. If they are in balance, the additional coin belongs to the group 9, 10, 11, or 12. Our second option is to weigh the numbers 9, 10, and 11 against the numbers 1, 2, and 3 (1). If they balance, you will know that the number 12 is a different coin, and you can simply weigh it in comparison to any other coin to determine its weight. (2) 9,10,11 is heavy. You are aware that the alternate coin is a heavy 9, 10, or 11 in this situation. Just compare 9 and 10, and if they balance, 11 is the heavier coin. If not, the heavier one is the heavy coin. (3) 9,10,11 is light. Continue as in the preceding step, but look for the light coin instead. That was the easy part. If the first coin, which should weigh 1, 2, 3, and weighs 5, 6, 7, and 8, does not balance, then any of these coins could be a different coin. We must now keep track of which side is heavier for each of the upcoming weighings in order to move on. Suppose that 5,6,7,8 is the heavy side. We now weigh 1,5,6 against 2,7,8. If they are equal, the other coin is either a 3 or a 4. Weigh 4 against 9, a known good coin. The alternate coin is 3, if they balance, otherwise it is 4. We can determine the weight of the offending coin based on the direction of the tilts. Now, if the ratio of 1,5,6, and 2,7,8, where 2,7,8, is the heavy side, does not balance, either 7 or 8 would be a different, heavy coin, or 1 would be a different, light coin. For the third weighing, weigh 7 against 8. Whichever side is heavy is the different coin. If they balance, then 1 is the different coin. If weighing 1, 5, and 6 versus 2, 7, and 8 reveals that 1, 5, and 6 are on the heavier side, then either 5 or 6 is a different heavy coin or 2 is a different light coin. Weigh 5 against 6. The heavier one is the different coin. If they balance, then 2 is a different light coin.
Difficulty 
Popularity 
A thief was running from the police after the biggest theft the town saw. He took his guard in one of the thirteen caves arranged in a circle. Each day, the thief moves either to the adjacent cave or stay in the same cave. Two cops goes there daily and have enough time to enter any two of the caves out of them. How will the cop make sure to catch the thief in minimum number of days and what are the minimum number of days?
Difficulty Popularity There are three bags.The first bag has two blue rocks. The second bag has two red rocks. The third bag has a blue and a red rock. All bags are labeled but all labels are wrong.You are allowed to open one bag, pick one rock at random, see its color and put it back into the bag, without seeing the color of the other rock. How many such operations are necessary to correctly label the bags ?
Just one example: If you receive Blue Rock with the label “blue+red,” it will be red because all other labels are incorrect. In this way u can logically solve this puzzle.
1. Fill 5 liters jar ( 5l-jar:5, 3l-jar:0) 2. Transfer to 3 liters pail (5l-jar:2, 3l-jar:3) 3. Empty 3 liters jar ( 5l-jar:2, 3l-jar:0) 4. Transfer 2q (5l-jar:0, 3l-jar:2) from a 5 to a 3 pail. Fill 5 liters pail(5l-jar:5, 3l-jar:2) 6. Transfer 1q from 5 pail to 3 pail(5l-jar:4, 3l-jar:3).
The Cube is emphasized as being more than just a toy or a puzzle in Google’s subsequent video. “Erno’s cube is a question waiting to be answered,” as the saying goes And amazing things happen when the right person asks the right question. Additionally, they suggest a few additional “beautiful questions” for me to add to my list.
Erno Rubik is obviously a card-carrying Master Questioner, which I didn’t know about. Anyone who has read my book will recognize Rubik’s statement in the video:
In addition to honoring Budapest-based educator Erno Rubik on the 40th anniversary of his Rubik’s Cube (created by him in 1974; made public in the 1980s), Google recently released a fantastic short video (see below) about the value of curiosity and questioning. It also serves as a call to foster the next generation of “scientists, engineers, artists, designers, inventors, or something no one’s ever been before… but you can bet we’re going to need ”.
FAQ
What are the 7 steps to solving a Rubik’s cube?
- Step 1: Create White Cross. Begin by holding the cube with the white face up.
- Step 2: Solve White Corners. …
- Step 3: Solve Middle Layer. …
- Step 4: Create Yellow Cross. …
- Step 5: Swap Yellow Edges in Top Layer. …
- Step 6: Position Yellow Corners. …
- Step 7: Solve Final Layer Corners.
Which method is fastest in Rubik’s cube?
The Fridrich method, also known as the CFOP method (cross, F2L, OLL, PLL), was developed by Jessica Fridrich as a quick way to solve the Rubik’s Cube.
What does Rubik’s cube symbolize in life?
The majority of people can’t solve a Rubik’s Cube in a flash. It takes time. You’ll make errors, choose the wrong path, and regret ever setting eyes on the thing. But only those who are willing to persevere and push past their frustrations will find success.
What does XYZ mean in Rubik’s cube?
Cube rotations are denoted by the letters X, Y, and Z. X signifies rotating the cube in the R direction. Y denotes the cube’s rotation in the U direction. Z denotes the cube’s rotation in the direction of F. These cube rotations are incorporated into algorithms to improve their speed and smoothness.
