Brain Teasers

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The British are Coming!

Category:	Trivia
Submitted By:	solarsistim321
Fun:	(1.73)
Difficulty:	(2.92)

Matrices were used very often as codes during WWII. It was an excellent way to encode secret messages. Unless someone has the matrix with which to decode the other matrices it would be nearly impossible to uncode the message. Lucky for you, you have all the information you need to decode the message. Let's see if you can!

Your main matrix is:

[-3 -2]
[ 4 3]

Decode the message:

11, 12, -15, -10, -3, 0, 8, 6, -75, -50, -32, -21, -26, -16, 80, 60, -9, -1, 36, 27, -18, -12, 94, 71, 76, 57, -11, -7. - -44, -29, -15, -6, 72, 54, 73, 56, 57, 44, -15, -10.

Answer:

One if by land, two if by sea. - Paul Revere.

You were given a 2x2 matrix (rows x columns). Since it has two rows, you will need to group the code in matrices of 1x2. This gives you:

[11 12][-15 -10][-3 0][8 6][-75 -50][-32 -21][-26 -16][80 60][-9 -1][36 27][-18 -12][94 71][76 57][-11 -7]. - [-44 -29][-15 -6][72 54 ][73 56][57 44][-15 -10].

From here you need to proceed by multiplying each of these matrices by the inverse of your main matrix. To find the inverse you first will need to find your determinate. To do this you multiply the top right and bottom left numbers and subtract it from the product of the top left and bottom right numbers. Your determinate is -1. -1 is then multiplied by each integer in your matrix, giving you:

[ 3 2]
[-4 -3]

You then proceed to switch the top left and bottom right numbers and reverse the sign on your other two numbers. From here you multiply each of the numbers in the matrix by your determinate. Your new matrix is:

[-3 -2]
[ 4 3]

You need to multiply the two numbers in the 1x2 matrices by the first two integers in your 2x2 main matrix. For example:

[11 12]
*
[-3 -2]
[ 4 3]

You would need to take [11*-3 + 12*4 11*-2 + 12*3]. You would get [15 14]. If you proceed using the same process through all of the 1x2 matrices, your new code would be:

[15 14][5 0][9 6][0 2][25 0][12 1][14 4][0 20][23 15][0 9][6 0][2 25][0 19][5 1]. - [16 1][21 12][0 18][5 22][5 18][5 0].

Each number represents its corresponding letter, for example A=1, B=2, C=3, etc. All you need to do then is substitute each number with its corresponding letter to get your answer.

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Comments on this teaser


Posted by solarsistim321	08/19/09
Whew! Second worst teaser on the site!! Not half bad :wink:

Posted by unklemyke	09/01/09
How is this trivia? Seems to me it wants to be in Math or Cryptography, nein? :-?

Posted by nidhikaila	12/09/09
superb teaser! like a morning cup of coffee... :-)

Posted by MusiK	12/21/09
Wow I think my brain just exploded:D I'm no good with this sort of stuff but otherwise, correct if I'm wrong, but I thought that Paul Revere didn't really say the well-known phrase in the title

Posted by Marple	08/25/10
who is paul revere?

Posted by MagicPurple	09/09/11
what's the worst teaser then? I thought this was the Trick category, so when it said look at the title, I thought the answer was the title. :lol: