Logic and Mathematics Test

LOGIC AND MATHEMATICS TEST Here you will find a series of exercises designed to assess your aptitude for solving logic and mathematics problems. Keep in mind that the goal here is not simply to discover the answer. The solution process has to be intriguing and fun for you. If you find out that solving this type of problem is a form of leisure, that is a good sign of aptitude to work in the area of exact sciences, among which is the profession of programmer. Have fun! Barbado.
1) THE BALLS AND THE SCALE You have 8 table tennis balls and a Double-Pan Balance Scale. Seven of the balls are exactly the same weight, but one is slightly heavier than the others. What is the minimum number of times you need to use the scale to know for sure which ball is the heavier one, not counting on luck? ANSWER:

2) LOGICAL SEQUENCE Given the following logical sequence of numbers: 3 - 10 - 12 - 13 - 20 - [??] What is the next number in the sequence? ANSWER:

3) HALF COW A young and inexperienced cowboy was given the task of bringing a herd of cattle from the farm where he worked, to sell them in the city. However, on the way he had the difficult mission of crossing three large rivers, for which there were no bridges. When crossing the first river, the strong current carried away half the cows he was leading, plus half a cow, and they were lost from the herd. When crossing the second river, the strong current again carried away half the remaining cows he was leading, plus half a cow, and they were lost from the herd. When crossing the third river, the strong current again carried away half the remaining cows he was leading, plus half a cow, and they were lost from the herd. Upon arriving at the city market, the poor cowboy led a single cow. With how many cows did he start the journey? ANSWER:

4) THE AGE OF THE GIRLS A young man, who was famous in his city for his great mathematical ability, was calmly walking down the street, when he was challenged by a lady to guess the ages of her 3 daughters. The boy then asks for a hint, and she says that the result of multiplying their age is equal to 36. The boy says that with only this information, it is not possible to determine their age. The lady then says that their ages added together are equal the number of house just accross the street. The boy then goes there, looks at the number and says that it is still impossible to determine the age of the three girls precisely. The lady looks at him suspiciously and says that the oldest daughter has green eyes, and then the boy answers precisely their age! How old are the three girls? ANSWER:

5) THE SLUG ON THE WALL A slug patiently tries to climb a 7-meter wall. During the day it rises 3 meters. But while it sleeps, at night, it slips 2 meters. Assuming she started climbing the wall very early today, how many days will it take her to reach the top of the wall? ANSWER: