# 10 mathematical and logical problems of interviewing large companies

Not so easy to find a good job, excellent - even more difficult. And to get a cherished place in some vast and illustrious corporation, so it is generally necessary to be not only a great professional but also a sharp-witted original man with a strong sense of humor and no less-developed logic. Answers can be found at the end of the article.

### Question from the Google

Problem 1: You have 8 balls of the same type and size.

Question: how to find the heavier ball, using the scale and having the right to just two weigh?

### Question from as Adobe

Problem 2: You have 50 motorcycles with fuel in the tank, which is enough for 100 km ride.

Question: how far using these 50 motorcycles you can call (noting that initially they are in the same notional point)?

### Questions from Apple's

Task 3: Sheldon Cooper reached in game quest in pursuit of treasure to the last ditch. In front of him - two doors, one leads to the treasure, the second - to the deadly dangerous maze. Each door is a guard, each of them knows which door leads to the treasure. One of the guards never lies, the other - always lying. Sheldon does not know which one of them is a liar, and who is not. Before choosing a door, you can ask only one question and only one guard.

Question: I should ask Sheldon a guard to get to the treasure?

### Question from Qualcomm's

This puzzle told the applicant, is interviewed as a senior systems engineer. He noted in the description of the problem, he had his answer, about which he had a long argument with the person being interviewed. So, Objective 4: Suppose we have going 10 packet data transmission over a wireless network. The channel is not very high quality, so that there is a probability of 1/10 that the data packet is transmitted. The transmitter always knows the success or failure of data packet has been transmitted. When the transfer is unsuccessful, the transmitter will send the package as long as it succeeds. Question: What is the bandwidth?

### Questions from "Yandex"

This task is proposed to solve for the entry in the "Data Analysis School" in February 2014.

Problem 5: The game consists of identical and independent Konov, in each of which gain occurs with probability X. When a player wins, he gets $ 1, and when losing - pays $ 1. Once it reaches the capital value of N dollars, he is declared the winner and removed from the casino.

Question: Find the probability that the player will sooner or later lose all the money, depending on its initial capital K.

The following problem is proposed to solve the developers at the interview, and it is more directly related to programming than the previous examples.

Task 6: You have a morphological dictionary volume of about 100,000 entries in which the words of perfect and imperfect species placed in separate articles (that is, "to do" and "do" are considered different dictionaries included). You need to find in the dictionary such species pairs and "glue" in the same article.

Question: Describe the overall scenario of solving this problem and the approximate search algorithm species pairs.

### Questions from the Microsoft

Target 7: You have an infinite supply of water and two buckets - 5 liters and 3 liters.

Question: how do you measure out 4 liters?

Problem 8: You have two pieces of rope. Each such length that when set fire to it at one end, it will burn exactly 60 minutes.

Question: Having only one box of matches, how to measure with the help of two segments a rope 45 minutes? (Can not tear the rope.)

Q-bonus

Some attribute it to the authorship of scientific genius Albert Einstein, others - Lewis Carroll. Target 9: there are five houses on the street. The Englishman lives in the red house. The Spaniards have a dog. In the green house drinks coffee. The Ukrainian drinks tea. The green house is immediately to the right of the white house. Anyone who smokes Old Gold, breeds snails. The yellow house smoke Kool. In the central house drinks milk. The Norwegian lives in the first house. A neighbor of the one who smokes Chesterfield, contains a fox. In the house next to the one in which include horse-smoking Kool. Anyone who smokes Lucky Strike, drinking orange juice. Japanese smokes Parliament. The Norwegian lives next to the blue house. Each house is painted in a different color in each house lives a representative of a separate nationality, everyone - your pet, a favorite brand of cigarettes and a drink.

Question: Who is drinking water? Who keeps a zebra?

Answer 1: Collect 6 balls, divide them into groups of 3 balls and put on the scales. Group heavier ball tipped. Select any two of these three balls and weigh. If the heavy ball is among them, you know it; if they weigh the same - heavy one that stayed. If the heavier ball was not in groups of 3 balls, he - among the remaining 2

Answer 2: The simple answer: to have them all at the same time and travel 100 km. But there is another solution. First, move all the bikes for 50 km. Then pour the fuel from the half to the other half of the motorcycle. You thus - 25 motorcycles with a full tank. Keep driving for another 50 km and repeat the procedure. So you can get up to 350 km (without taking into account the fuel, which will remain on the "extra" when the motorcycle section 25 in two)

Answer 3: Any of the guards can ask a question: "What's the door, according to another guard, right?". If he asks an honest, then get data about which door leads to the maze, because the guard-liar always lie. If he asks the guard, a liar, then know which door leads to the maze, because the sovret on the door, which will show an honest guard Answer 4: If the user version, the answer had to be: 9 pps. But the person who conducted the interview, did not agree with him, however, he did not give an answer, saying only that "due to retransmission, the bandwidth must be reduced by more than 1/10"

Answers 5 and 6 on the "Yandex" problem, unfortunately, is not known.

Answer 7: Fill a five-liter bucket of water and pour the water in the three-liter. You are now in a small 3 liter bucket and 2 - in the large. Empty the small bucket and pour back the remaining 2 liters from the large. Refill the large bucket and pour out the water in the small. There are already 2 liters of water, so it will have to pour a liter of all, and in a big stay of 4 liters

Answer 8: One of the segments is ignited at both ends, at the same time ignited the second segment, but at one end. When the first segment burn down completely, it may take 30 minutes from the first well will be a 30-minute segment. Burning it at both ends, we get 15 more minutes

Answer 9: The Japanese live zebra, Norwegian drinking water