Riddles are a fun way to pass the time, riddles that require the use of our intellectual capacity, our reasoning and our creativity in order to find their solution. And they can be based on a large number of concepts, including areas as complex as mathematics. That is why in this article we will see a series of mathematical and logical puzzles, and their solutions
This is a dozen mathematical puzzles of varying complexity, extracted from various documents such as the book Lewi’s Carroll Games and Puzzles and different web portals (including the YouTube channel on mathematics “Deriving”).
1. Einstein’s riddle
Although it is attributed to Einstein, the truth is that the authorship of this riddle is not clear. The puzzle, more about logic than mathematics itself, reads as follows:
“On a street there are five houses of different colors, each occupied by a person of a different nationality. The five owners have very different tastes: each of them drinks a type of drink, smokes a certain brand of cigarette and each has a pet that is different from the others. Taking into account the following clues: The British man lives in the red house The Swede has a dog as a pet The Dane drinks tea The Norwegian lives in the first house The German smokes Prince The green house is immediately to the left of the white one The owner of the green house drinks coffee The owner who smokes Pall Mall raises birds The owner of the yellow house smokes Dunhill The man who lives in the center house drinks milk The neighbor who smokes Blends lives next door to the one who has a cat The man who has a horse lives next to the one who smokes Dunhill The owner who smokes Bluemaster drinks beer The neighbor who smokes Blends lives next to the one who drinks water The Norwegian lives next to the blue house
Which neighbor lives with a pet fish at home?
2. The four nines
Simple riddle, it tells us “How can we make four nines equal a hundred?”
3. The bear
This puzzle requires knowing a little geography. “A bear walks 10 km south, 10 east and 10 north, returning to the point from which it started. What color is the bear?”
4. In the dark
“A man wakes up at night and discovers that there is no light in his room. He opens the glove drawer, in which there are ten black gloves and ten blue ones How many should you take to make sure you get a pair of the same color?”
5. A simple operation
A seemingly simple riddle if you realize what it refers to. “At what point will the operation 11+3=2 be correct?”
6. The problem of the twelve coins
We have a dozen visually identical coins, of which all weigh the same except one. We don’t know if it weighs more or less than the others. How will we find out which one it is with the help of a scale on at most three occasions?
In the game of chess, there are pieces that have the possibility of passing through all the squares of the board, such as the king and queen, and pieces that do not have that possibility, such as the bishop. But what happens with the horse? Can the knight move around the board in such a way that it passes through each and every one of the squares on the board?
8. The rabbit paradox
This is a complex and ancient problem, proposed in the book “The Elements of Geometrie of the most ancient Philosopher Euclides of Megara”. Assuming that the Earth is a sphere and that we pass a rope through the equator, in such a way that we surround it with it. If we lengthen the rope one meter, in such a way that forms a circle around the Earth Could a rabbit fit through the gap between the Earth and the rope? This is one of the mathematical puzzles that require good imagination skills.
9. The square window
The following mathematical puzzle It was proposed by Lewis Carroll as a challenge to Helen Fielden in 1873, in one of the letters he sent him. In the original version it talked about feet and not meters, but the one we give you is an adaptation of this. Pray the following:
A nobleman had a living room with a single window, square and 1m high by 1m wide. The nobleman had an eye problem, and the headlight let in a lot of light. He called a builder and asked him to alter the window so that only half the light came in. But it had to remain square and with the same dimensions of 1×1 meters. He also couldn’t use curtains or people or stained glass, or anything like that. How can the builder fix the problem?
10. The monkey riddle
Another riddle proposed by Lewis Carroll.
“On a simple frictionless pulley, a monkey is hung from one side and a weight from the other that perfectly balances the monkey. Yeah the rope has no weight or friction “What happens if the monkey tries to climb the rope?”
11. String of numbers
This time we find a series of equalities, of which we have to solve the last one. It is easier than it seems to be. 8806=6 7111=0 2172=0 6666=4 1111=0 7662=2 9312=1 0000=4 2222=0 3333=0 5555=0 8193=3 8096=5 7777=0 9999=4 7756=1 6855= 3 9881=5 5531=0 2581=?
12. Password
Police are keeping a close eye on a den of a gang of thieves, which have provided some type of password to enter. They watch as one of them comes to the door and knocks. From inside, 8 is said and the person answers 4, a response to which the door opens.
Another arrives and they ask him for the number 14, to which he answers 7 and also passes. One of the agents decides to try to infiltrate and approaches the door: from inside they ask him for the number 6, to which he answers 3. However, he must retreat since not only do they not open the door but he begins to receive shots from the door. inside. What is the trick to guess the password and what mistake has the police made?
13. What number does the series follow?
A riddle known for being used in a school admission exam in Hong Kong and for there being a tendency that children tend to perform better in solving it than adults. It is based on guessing What number is the occupied parking space in a parking lot with six spaces? They follow the following order: 16, 06, 68, 88, ? (the occupied square that we have to guess) and 98.
A problem with two possible solutions, both valid. It is about indicating what number is missing after seeing these operations. 1+4=5 2+5=12 3+6=21 8+11=?
Solutions
If you have been left wondering what the answers to these riddles are, you will find them below.
1. Einstein’s riddle
The answer to this problem can be obtained by making a table with the information we have and discarding from the clues The neighbor with a pet fish would be the German.
2. The four nines
9/9+99=100
3. The bear
This puzzle requires knowing a little geography. And the only points at which, following this path, we would reach the point of origin are at the poles In this way, we would be facing a (white) polar bear.
4. In the dark
Being pessimistic and anticipating the worst case scenario, the man should take half plus one to ensure he gets a pair of the same color. In this case, 11.
5. A simple operation
This riddle is solved very easily if we take into account that we are talking about a moment. That is, time. The statement is correct if we think about the hours: If we add three hours to eleven, it will be two.
6. The problem of the twelve coins
To solve this problem we must use the three occasions carefully, rotating the coins. First we will distribute the coins into three groups of four. One of them will go on each arm of the scale and a third on the table. If the scale shows a balance, this means that the fake coin with a different weight is not among them but among those on the table Otherwise, it will be in one of the arms.
In any case, on the second occasion we will rotate the coins in groups of three (leaving one of the originals fixed in each position and rotating the rest). If there is a change in the tilt of the scale, the different coin is among those we have rotated.
If there is no difference, it is between those that we have not moved. We remove the coins that there is no doubt are not the fake ones, so on the third attempt we will have three coins left. In this case, it will be enough to weigh two coins, one on each arm of the scale and the other on the table. If there is balance, the false one will be the one on the table and if not, and based on the information extracted on previous occasions, we will be able to say what it is.
7. The horse path problem
The answer is affirmative, just as Euler proposed. To do this, he should do the following path (the numbers represent the movement in which he would be in that position).
The answer to whether a rabbit would pass through the gap between the Earth and the rope by lengthening the rope by a single meter is affirmative. And it is something that we can calculate mathematically. Assuming that the Earth is a sphere with a radius of around 6.3000 km, r=63000 km, although the rope that completely surrounds it has to be of considerable length, expanding it by a single meter would generate a gap of around 16 cm . This would generate that a rabbit could comfortably fit through the gap between both elements
To do this we have to think that the rope that surrounds it will originally measure 2πr cm in length. The length of the rope by lengthening it by one meter will be. If we lengthen this length by one meter, we will have to calculate the distance that the rope must be distanced, which will be 2π (r+extension necessary for it to be lengthened). Then we have that 1m= 2π (r+x)- 2πr. Doing the calculation and solving for x, we obtain that the approximate result is 16 cm (15.915). That would be the gap between the Earth and the rope.
9. The square window
The solution to this riddle is make the window a rhombus Thus, we will continue to have a 1*1 square window without obstacles, but through which half the light would enter.
The answer to this question is simple. Only we have to look for the number of 0s or circles that are in each number For example, 8806 has six since we would count the zero and the circles that are part of the eights (two in each) and the six. Thus, the result of 2581= 2.
12. Password
Looks are deceiving. Most people, and the police officer involved in the problem, would think that the answer the thieves ask for is half the amount they are asking about. That is, 8/4=2 and 14/7=2, which would only require dividing the number that the thieves gave.
This is why the agent answers 3 when asked about the number 6. However, that is not the correct solution. And what thieves use as a password It is not a numerical relationship, but the number of letters in the number That is, eight has four letters and fourteen has seven. In this way, in order to enter, the agent would have had to say four, which are the letters in the number six.
13. What number does the series follow?
This puzzle, although it may seem like a mathematical problem that is difficult to solve, in reality only requires observing the squares from the opposite perspective. And in reality we are facing an ordered row, which we are observing from a specific perspective. Thus, the row of seats that we are observing would be 86, 88, 89, 90, 91. In this way, The occupied square is 87
14. Operations
To solve this problem we can find two possible solutions, as we have said, both are valid. In order to complete it, you must observe the existence of a relationship between the different operations of the puzzle. Although there are different ways to solve this problem, below we will see two of them.
One of the ways is to add the result of the previous row to what we see in the row itself. Like this: 1+4=5 5 (the one from the result above)+(2+5)=12 12+(3+6)=21 21+(8+11)=? In this case, the answer to the last operation would be 40.
Another option is that instead of a sum with the immediately previous figure, we see a multiplication. In this case we would multiply the first figure of the operation by the second and then we would do the sum. Like this: 14+1=5 25+2=12 36+3=21 811+8=? In this case the result would be 96.
