SQL Puzzle 5: Prime Magic

Quite a few of you have read or attempted the previous puzzle SQL Puzzle 1: Magic Squares

As a quick reminder, when you have a 3 x 3 grid, a magic square is one where each row, column or diagonal add up to the same value. e.g.

magic-square

All the rows, all the columns and both diagonals each add up to 15.

In the previous puzzle I asked you to write SQL to find all the possible 3 x 3 magic squares. After originally coming across that idea I discovered all sorts of variants on the magic square theme.

This time, I’ll ask you to find write SQL to find just one 3 x 3 magic square, but in this case one composed only of prime numbers? They don’t have to be consecutive primes (though they do all have to be different), and to make things easier you can treat the number 1 as a prime if you want.

Have fun!

Previous Puzzles:
SQL Puzzle 1: Magic Squares
SQL Puzzle 2: Eight Queens
SQL Puzzle 3: Knights and Queens
SQL Puzzle 4: The Beale Papers

SQL Puzzle 4: The Beale Papers

I’ve not done a SQL puzzle for a while so thought it was getting overdue…

I set this one for my workmates a while ago and people found it quite fun.

The Beale Papers are a set of three ciphertexts which allegedly reveal the details of a buried treasure. The tale is that the treasure was buried by Thomas J. Beale in Bedford County, Virginia, USA back in the 1820s. He entrusted a box containing the ciphered messages to the care of a local innkeeper and then disappeared never to be seen again – his intent was that the papers could be passed on to his descendants and they could decode the messages and claim their rightful inheritance. The innkeeper passed the ciphertexts on to a friend before he died, and said friend spent the rest of his life trying to decipher them. He succeeded on the second message but failed on the others.

Treasure.png

Since the 19th century many attempts have been made to decipher the other messages and find the treasure. Even without cracking the code, treasure hunters have got out their shovels over the years to dig up parts of Bedford County without finding anything (as far as we know). Recently there are some claims to have solved the puzzle, but that the treasure was already gone.Of course there’s a good chance the whole thing is a hoax!

Your task is to repeat the deciphering of the second message, but to make it easier I’ll tell you the key.

Beale used an existing text as a key for the cipher in which he assigned a number to each word, 1 for the first word, two for the second and so on.

Then for each letter in the text he wanted to encode he randomly picked a word in the key that started with that letter, and then he enciphered the letter as the number for that word. Make sense?

For instance, if the key text was “now is the time” and the plain text is “tin”, then either (3 2 1) or (4 2 1) are valid encipherments.

The key text Beale used for encoding the second message was the United States declaration of independence. I’m going to leave you to source your own copy of this. Be aware that some of the real world issues with this task that you may come up include the fact that Beale may have made some inaccuracies in his ciphering, and the copy of the key text he used to code his text is unlikely to be exactly the same as the one you use. As such you may need to do some tweaking, spelling correction and perhaps logic to work out what some of the words are. Good luck if you choose to attempt this!

So, starting with the two variables below, write some SQL to decode the message (@CipherText ):

DECLARE @KeyText VARCHAR(MAX); 
DECLARE @CipherText VARCHAR(MAX);

SET @KeyText = '<Insert your copy of the declaration of independence here>';

SET @CipherText = '115, 73, 24, 807, 37, 52, 49, 17, 31, 62, 647, 22, 7, 15, 140, 47, 29, 107, 79, 84, 56, 239, 10, 26, 811, 5, 196, 308, 85, 52, 160, 136, 59, 211, 36, 9, 46, 316, 554, 122, 106, 95, 53, 58, 2, 42, 7, 35, 122, 53, 31, 82, 77, 250, 196, 56, 96, 118, 71, 140, 287, 28, 353, 37, 1005, 65, 147, 807, 24, 3, 8, 12, 47, 43, 59, 807, 45, 316, 101, 41, 78, 154, 1005, 122, 138, 191, 16, 77, 49, 102, 57, 72, 34, 73, 85, 35, 371, 59, 196, 81, 92, 191, 106, 273, 60, 394, 620, 270, 220, 106, 388, 287, 63, 3, 6, 191, 122, 43, 234, 400, 106, 290, 314, 47, 48, 81, 96, 26, 115, 92, 158, 191, 110, 77, 85, 197, 46, 10, 113, 140, 353, 48, 120, 106, 2, 607, 61, 420, 811, 29, 125, 14, 20, 37, 105, 28, 248, 16, 159, 7, 35, 19, 301, 125, 110, 486, 287, 98, 117, 511, 62, 51, 220, 37, 113, 140, 807, 138, 540, 8, 44, 287, 388, 117, 18, 79, 344, 34, 20, 59, 511, 548, 107, 603, 220, 7, 66, 154, 41, 20, 50, 6, 575, 122, 154, 248, 110, 61, 52, 33, 30, 5, 38, 8, 14, 84, 57, 540, 217, 115, 71, 29, 84, 63, 43, 131, 29, 138, 47, 73, 239, 540, 52, 53, 79, 118, 51, 44, 63, 196, 12, 239, 112, 3, 49, 79, 353, 105, 56, 371, 557, 211, 505, 125, 360, 133, 143, 101, 15, 284, 540, 252, 14, 205, 140, 344, 26, 811, 138, 115, 48, 73, 34, 205, 316, 607, 63, 220, 7, 52, 150, 44, 52, 16, 40, 37, 158, 807, 37, 121, 12, 95, 10, 15, 35, 12, 131, 62, 115, 102, 807, 49, 53, 135, 138, 30, 31, 62, 67, 41, 85, 63, 10, 106, 807, 138, 8, 113, 20, 32, 33, 37, 353, 287, 140, 47, 85, 50, 37, 49, 47, 64, 6, 7, 71, 33, 4, 43, 47, 63, 1, 27, 600, 208, 230, 15, 191, 246, 85, 94, 511, 2, 270, 20, 39, 7, 33, 44, 22, 40, 7, 10, 3, 811, 106, 44, 486, 230, 353, 211, 200, 31, 10, 38, 140, 297, 61, 603, 320, 302, 666, 287, 2, 44, 33, 32, 511, 548, 10, 6, 250, 557, 246, 53, 37, 52, 83, 47, 320, 38, 33, 807, 7, 44, 30, 31, 250, 10, 15, 35, 106, 160, 113, 31, 102, 406, 230, 540, 320, 29, 66, 33, 101, 807, 138, 301, 316, 353, 320, 220, 37, 52, 28, 540, 320, 33, 8, 48, 107, 50, 811, 7, 2, 113, 73, 16, 125, 11, 110, 67, 102, 807, 33, 59, 81, 158, 38, 43, 581, 138, 19, 85, 400, 38, 43, 77, 14, 27, 8, 47, 138, 63, 140, 44, 35, 22, 177, 106, 250, 314, 217, 2, 10, 7, 1005, 4, 20, 25, 44, 48, 7, 26, 46, 110, 230, 807, 191, 34, 112, 147, 44, 110, 121, 125, 96, 41, 51, 50, 140, 56, 47, 152, 540, 63, 807, 28, 42, 250, 138, 582, 98, 643, 32, 107, 140, 112, 26, 85, 138, 540, 53, 20, 125, 371, 38, 36, 10, 52, 118, 136, 102, 420, 150, 112, 71, 14, 20, 7, 24, 18, 12, 807, 37, 67, 110, 62, 33, 21, 95, 220, 511, 102, 811, 30, 83, 84, 305, 620, 15, 2, 10, 8, 220, 106, 353, 105, 106, 60, 275, 72, 8, 50, 205, 185, 112, 125, 540, 65, 106, 807, 138, 96, 110, 16, 73, 33, 807, 150, 409, 400, 50, 154, 285, 96, 106, 316, 270, 205, 101, 811, 400, 8, 44, 37, 52, 40, 241, 34, 205, 38, 16, 46, 47, 85, 24, 44, 15, 64, 73, 138, 807, 85, 78, 110, 33, 420, 505, 53, 37, 38, 22, 31, 10, 110, 106, 101, 140, 15, 38, 3, 5, 44, 7, 98, 287, 135, 150, 96, 33, 84, 125, 807, 191, 96, 511, 118, 40, 370, 643, 466, 106, 41, 107, 603, 220, 275, 30, 150, 105, 49, 53, 287, 250, 208, 134, 7, 53, 12, 47, 85, 63, 138, 110, 21, 112, 140, 485, 486, 505, 14, 73, 84, 575, 1005, 150, 200, 16, 42, 5, 4, 25, 42, 8, 16, 811, 125, 160, 32, 205, 603, 807, 81, 96, 405, 41, 600, 136, 14, 20, 28, 26, 353, 302, 246, 8, 131, 160, 140, 84, 440, 42, 16, 811, 40, 67, 101, 102, 194, 138, 205, 51, 63, 241, 540, 122, 8, 10, 63, 140, 47, 48, 140, 288';

 

I’ll finish this post with an excerpt from the comments on a blog I found where someone claims to have decoded the other two texts as well, and know where the treasure is:
TreasureFound

Have fun!

Previous puzzles on this blog:
SQL Puzzle 1: Magic Squares
SQL Puzzle 2: Eight QueensSQL Puzzle 3: Knights and Queens

Credit to Programming Praxis where I first saw a version of this puzzle – and where you can find many more!

SQL Puzzle 3: Knights and Queens

I thought I’d do another chess puzzle this month. This one is a variant on the Eight Queens problem:

SQL Puzzle 2: Eight Queens

 

Given the standard 8×8 chessboard, place an equal number of Knights and Queens such that no piece is attacked by another. What’s the maximum number of Knights and Queen’s you can place? Obviously you should use SQL to find the answer!

 

I’m sure you all know how a knight moves and attacks in chess, but just in case here’s a diagram:

 

 knight_move

 

The white circles show each possible move for the knight, i.e. it can move two squares in one direction and then 1 square perpendicular to that (or vice-versa). An “L” shape.

 

Have fun!

SQL Puzzle 2: Eight Queens

This puzzle was first proposed in 1848 by a composer of chess puzzles called Max Bezzel and has since spawned much analysis and many variants. Simply phrased, it goes as follows:

“Can you place 8 queen’s on a standard (8×8) chessboard so that no two queen’s threaten each other?”

(Just in case, I’ll remind you a queen can move and attack any number of squares in a straight line –  horizontally, vertically, or diagonally)

Here’s one example solution:

8queens

By all means have some fun trying to find extra solutions to this with pencil and paper or chessboard, however we do have computers (and SQL!) these days, so this month’s challenge is to try find ALL the possible solutions to this puzzle using T-SQL.

I’m a bit of a closet chess enthusiast, so expect more in this theme!

Enjoy 🙂

SQL Puzzle 1: Magic Squares

This is the first in what I hope will be a semi-regular series of recreational puzzles where SQL can be used to find the answer. I set these puzzles on occasional Fridays in my workplace, and as I now have quite an archive I thought I should start sharing them with a wider audience.

I came up with the idea for this puzzle involving Magic Squares by accident while trying to do something different – and getting it wrong! For a moment I thought I’d had an original idea but then it was “Hang on – I’m sure I must have seen this before.”

A bit of googling and that thought was proved right – I’m just not that original. In fact the first documented instance of these appears to be the Chinese legend of Lo Shu – possibly dating back as far as 650BC. I was only beaten by the best part of three millennia…

You may have seen these before at some point – but hopefully long enough ago that you don’t know all the answers! Possibly like me they ring a bell for you but you can’t remember exactly where from.

A Magic Square is a square grid e.g. 1×1, 2×2, 3×4, 4×4…. or n x n, where numbers are placed in each square in the grid such that if you add up the numbers in each column, row, or diagonally they all add up to the same total.

Usually you use consecutive numbers starting from 1 (placing each number just once), so in the 2 x 2 grid you would place the numbers 1 to 4, in the 3 x 3 the numbers 1 to 9 – and so on.

Here’s the 1 x1 grid:

MagicSquare1

I thought I’d be generous and give you that one for free 😉

So my first question is can you find a solution (with the numbers 1 to 4) to the 2 x 2 grid:

MagicSquare2

Having explored that possibility (not for too long I hope!) the meat of this puzzle is to find solutions to the 3 x 3 grid using the numbers 1 to 9:

MagicSquare3

In fact, using SQL, can you not just find one solution, but all the possible solutions? How many are there?

Share your attempts and answers in the comments.

Have fun 🙂