To have a good time with women, we need money… a lot of money!
so we have:
Women = money2
But money is the root of evil. So we have:
Money = √ evil.
Substitute and we have:
Women = √evil2
The root and the square disappear, so we have:
Women = evil!
(women are wonderful creatures, and of course the above is only intended to bring laughter and not to belittle women.)
Leonhard Euler created the following magic square:
The above magic square of order 8 has the following properties:
It’s called a magic square, although the diagonals don’t sum to 260. It’s also the solution to the chess problem I’ve already posted.
The following magic square of order 8 was constructed by Benjamin Franklin, the famous scientist and writer of the 1700s.
Notice that each row or column of the magic square has a sum of 260. Also , half of each row or column has a sum of 130. In addition, if we take the halves of the diagonals in twos, “arcs” are formed which all have the same sum which also equals 260.
In many layouts of the square the numbers add up to 260.
It is attributed to A.W.Johnson, of which more details are not known, and is known as the magic square of the apocalypse, (of order 6), as the sum that appears in each column, row and diagonal is 666!!!!
The following magic square of order 4 has a sum of the numbers of each column, row and both diagonals equal to 176. (Picture 1)
Now, if we were to put a mirror on the left and look at its reflection, we would have a new magic square… (Picture 2)
If we again calculate the sum of the numbers of each column, row and two diagonals, we would again see that it is equal to 176.
If we take the original square again and turn it upside down, we will again have a new magic square, which, if we again calculate the sum of the numbers of each column, row and both diagonals, we will again see that it is equal to 176. (Picture 3)
Now, if we were to put a mirror on the left, and in it, and see its reflection, we would have a new magic square… (Picture 4)
If we again calculate the sum of the numbers of each column, row and both diagonals, we would again see that it is equal to 176.
Ηow can you and the knight pass through all the squares of the board, but using only once each checker, starting from the first square in the left corner?
This problem was created by Leonhard Euler. (15 April 1707 – 18 September 1783) was a Swiss polymath who was active as a mathematician, physicist, astronomer, logician, geographer, and engineer.
A magic square is a table of numbers that, if you add all the numbers in each row and column and in each of its two diagonals, adds up to the same sum and called magic constant. A magic square is also the below.
As we can see, in this magic square, all the rows, columns and diagonals add up to 111!
43+1+67=111, 61+37+13=111, 7+73+31=111,
43+61+7=111, 1+37+73=111, 67+13+31=111,
43+37+31=111, 67+37+7=111
In the below magic square of order 3, (The magic square 4 by 4 is of order 4, the magic square 5 by 5 is of order 5, the magic square 6 by 6 is of order 6, etc. ), it is interesting that all the numbers in the table are singular.
The first record of a magic square, (of order 3), appears in Ancient China in the 5th century B.C. A legend says that this magic square of the numbers 1 to 9 was a gift to the Chinese emperor Yu from a turtle of the Lo River, and this magic square is still used today as an amulet.
The magic square that was on the turtle is the below. This magic square has a sum of 15, in all the numbers in each row and in each column and in each of its two diagonals.
Albrecht Dürer, ( Albrecht Dürer, born 21 May 1471, died 6 April 1528), was a German painter, engraver and mathematician, and creator of the magic square of 34 of order 4.
This magic square makes its appearance, in his own engraving of 1514, “Melancholy”.
We can see that it is a magic square that all the lines add up to 34:
16+3+2+13=34, 5+10+11+8=34, 9+6+7+12=34, 4+15+14+1=34.
We see that all the columns also make 34:
16+5+9+4=34, 3+10+6+15=34, 2+11+7+14=34, 13+8+12+1=34.
We see that the diagonal rows also add up to 34:
16+10+7+1=34 and 13+11+6+4=34.
So far, it has the properties that all magic squares have… but the surprises of this square don’t stop there!!!
We see that if we divide the square into four, each piece comes out to 34:
16+3+5+10=34, 2+13+11+8=34, 9+6+4+15=;34, 7+12+14+1=34.
We see that the four end numbers add up to 34: 16+13+4+1=34. The four central squares add up to 34: 10+11+6+7=34. We see that the middle numbers of the first and last row, yield 34: 3+2+15+14=34. Also the middle numbers of the first and last columns, yields 34: 5+9+8+12=34.
We see that the first four squares clockwise, after the corners, make 34: 3+8+14+9=34. Also, the first four squares counterclockwise, after the corners make 34: 2+12+15+5=34.
We see that the squares enclosing the opposite corners make 34:
5+3+14+12=34 and 9+15+2+8=34.
The sum 34, appears in other formations on the square as well…
Finally, on the last line we see the numbers: 4,15,14,1.
Albrecht Dürer created the magic square in 1514.
His surname in German starts with the 4th letter of the alphabet, while his name starts with the 1st letter!
Why would the sum be 34?
1+2+3+4+5+6+7+8+9+10+11+12+13+14+15+16=136,
136/4=34, so the minimum magic square 4*4, must add up to 34…
Albrecht Dürer was very proud of his creation, and as we have seen, he was not wrong!!!
Here’s what I’ll start you off with:
Image website, /a/p9wVFJM
Have fun 😀
The Gordian Knot was the intricate knot that was tied to the chariot of King Gordius, who was the father of Midas. Gordius had seen an eagle sitting on the yoke of the chariot he was ploughing and took it as an omen, and later when he confessed to a girl who was a fortune teller what had happened, she told him when he came to Phrygia with the chariot, to sacrifice to Zeus. Gordius fell in love with her, married her and had a son Midas. An oracle said that the Phrygians would have to make a king who would come to the country in a chariot, in order to stop the civil war between them. So when Gordius came with his wife and his son Midas to this place, they made him king of Phrygia, and he stopped the rebellion. Later he was succeeded by his son, Midas. To honor Zeus, in addition to the necessary sacrifice, Gordios left his chariot as a tribute to the god. The chariot was tied with a rope of skull bark to the old palace of the kings of Phrygia, in the city of Gordian, and no one could untie it. Tradition said that whoever untied it would rule Asia. When Alexander the Great arrived in Gordium, he heard about the Gordian Knot, examined it and managed to untie it. One version says that he took his sword and cut it saying: “what cannot be untied, can be cut.” This, although it is the most popular version, is the least likely. Another version, according to Arrian and Plutarch, say that there was an eyewitness, Aristobulus, who saw that Alexander the Great, simple took the pin out of the steering wheel of the chariot and the knot that held on it, untied by itself. Today when we say that a problem is like the “Gordian Knot” we mean that it is a difficult and intractable problem. (But which can either have a very simple solution, or it will take extreme measures to solve it).
The image below shows some nautical knots.
I like listening to rap music a lot, but more specifically, Tyler, the Creator’s music. I thought it’d be a good idea to make a short and difficult puzzle about him just for fun.
The answer is one word. Good luck.
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