In a game for two players, 23 sticks are placed on a table and each opponent will alternately take one, two or three sticks at a time, as they prefer. The player who is forced to take the last stick will lose. What strategy can be followed to always win? Solution The player who leaves the last five sticks will win because his opponent must take 1, 2 or 3 and leave 4, 3 or 2 sticks respectively on the table so it will be enough to take 3, 2 or 1 to leave a single stick that the other player will take.
If all the boys sit on one of the rocking arms, how many girls should sit on the other end to keep their balance? To solve the puzzle we must assume that the distance of the children to the center of the rocker is not relevant. All boys are supposed to have the same "X" weight and all girls weigh the same "Y".
Police arrived at Cabbage Street in Brussels, after reports that an unusually large copy of Strangalia Maculata, the beetle has been seen running down the street, scaring shoppers. Before being able to catch it, the insect mysteriously disappeared during a downpour. It has not been seen since.
They say that when asking Albert Einstein about the number of disciples he had, he answered the following: Half of them study mathematics, a fourth physical part, a seventh part remain silent and there are also three women. How many disciples did Einstein have? Solution If we call X the number of disciples, we can deduce the following equation from the statement: From where we deduce that it had X = 28 disciples.
Charlie and Freddie have taken to wash the necks and cuffs of their shirts that add thirty pieces in total. Freddie explains to the clerk that his package contains half of the cuffs and a third of the necks and that it should cost twenty-seven cents. As four fists cost the same as five necks, the clerk, who is a bad mathematician, wants to know how much Charlie has to charge for the other package.
Today we are going to do a craft in class. It is about joining all the points of a polytope with ropes to make a very beautiful picture like the one in the drawing. The circumference has 20 points marked in red so that each of the points joins each and every one of the rest of the points with a rope between them so that we have a section of rope between any two points.
What is the highest number such that when expressed in letters it contains the five vowels, without repeating them? For example, in the number “One billion three” (1,000,000,000.003), we lack the letter “a” Solution If we start with the largest number with a defined name, the Googol, we see that no number of this magnitude can meet the condition that the vowels are not repeated since it has three letters "o".
If you look at the figure you will see three groups of stripes one with gray tones, another with blue tones and the other with red tones. How many different shades of gray, red and blue can you count? Solution If you look closely you will see that there is a single gray tone, one blue and one red, although it seems that there are two shades of each.
When we ask Maria and her little sister for their ages they answer the following: If we add three times the difference of our ages to the difference of the cubes of our ages, we get another cube as a result. How old is Maria's sister? Solution Maria is 11 years old and her sister 7 since it is true that 11 3 - 7 3 = 1331 - 343 = 988 3 * (11 - 7) = 3 * 4 = 12 988 + 12 = 1000 1000 = 10 3
Formerly, to move heavy objects several logs of similar size were used that were placed under the object to be moved. This was pushed and the trunks rolled so that the object moved forward. The drawing shows four identical trunks that have a circumference of 1 meter each.
Sherlock Holmes has sent some secret documents in a safe whose combination is a number that is divisible by 1, 2, 3, 4, 5, 6, 7, 8 and 9 and is also the minimum number that meets this property. What is the secret key? Solution Calculating the least common multiple of all numbers from 1 to 9 we find that the secret key is 2520.
They say that when a great fortune teller, when building his new crystal ball, he wanted to know its resistance to falls. So he made three equal balls, kept one for him and handed the other two to his apprentice to whom he entrusted the mission of checking their resistance. For this he ordered him to go to the tallest building in the city with 117 stories high and said: you must go up to the first floor of the building and throw the ball through the window.
If I think of a number, I multiply it by 3, then I add 30, the result I have divided by 11, the result is 1 and in the end I divide it by 7 I get the number 2. What number was I thinking? Solution The easiest way to find the solution is to undo all the operations that have been performed.
A seventh of the tickets have been sold for the premiere of a play. If 240 tickets represent two thirds of unsold tickets, how many locations did the theater have for sale in total? Solution In total there were 420 locations. To find the solution you must solve the following equation: 2/3 x 6/7 y = 240, where y = 420.
The participants of a mathematical olympiad are occupying all the seats of a rectangular hall in which the seats are aligned in rows and columns. At the beginning of the test, a teacher suggests that they wish each other luck by shaking hands so that each of the contestants shakes hands with those who are next to him (front, back, sides and diagonally) and only these.
Does this phrase have? vowels. What number (expressed in letters) must be put in place of the question in order for the phrase to be true? Self-referential phrases are those that speak of themselves. You can see some examples on Wikipedia. Solution This phrase has twelve vowels
Surely everyone knows the problem of the man who had a barrel of honey to sell and who has a three-quart and a five-quart container. The seller meets a customer who wants to buy four quarters of honey exactly. It is simple to transfer the honey with both measures until reaching the required four quarters but exercise the gray matter of their brains and see if they can discover the minimum number of changes with which that problem can be solved.
Two cogwheels belonging to the gears of a watch have an arrow marked with the initial position as shown in the figure. The small wheel rotates clockwise and the large wheel, therefore, counterclockwise. If the big wheel has 73 teeth, how many full turns should the small gear turn so that the arrows match again?
Dr. Art tells the following story: "I just talked on the phone with my brother. He had no idea where I was when we started the conversation. As soon as I said" here is September 9 "he replied:" I know where are you "and he was right in which country I was." In which country was Dr.
In a piece of furniture there are three drawers, in each drawer there are seven boxes, in each box there are five jewelers and in each jeweler there are two bracelets. How many bracelets are in each drawer? Solution There are 7 x 5 x 2 = 70 bracelets in each drawer.
Sebastian arrives at a small town and decides to cut his hair. In this town there are only two hairdressers: the first one is very well groomed and has a nice haircut, the second one goes badly styled and his haircut is horrible. In an incomprehensible way Sebastian decides to cut his hair the second hairdresser.