Math problems submitted by Puzzle Prime’s community
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.
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!!!
This puzzle combines elements of Sudoku with spreadsheet formulas.
Basic Rules
You can play it here: https://www.sheetdoku.com/
Hope you enjoy this game!
Snow has started falling some time before noon at a constant rate. At noon you start plowing from city A to city B, removing the snow at a constant volume per minute. If at 1PM you are 2 miles away from from city A, and at 2PM you are 3 miles away from city A, when did the snow start falling?
Change 3659 to 8101 by changing one digit at a time. Sounds easy. There is a catch! All numbers have to be four-digit primes. There is a unique shortest solution in 6 changes. If you like it I can publish more.
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