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 Are we odd for liking this, too? (Posted on 2005-08-30)
In "Are we odd for liking this?" we were asked to decipher an encrypted message. Can you decipher this message too?

57249994402124186529762
56227185287614394317684
72245794427434367112219
38125347227414186714489
63634187664324288447732

 See The Solution Submitted by Erik O. Rating: 3.3333 (3 votes)

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 Puzzle Solution Comment 18 of 18 |

At the outset, we add the numbers in a given column and reduce the addition result in mod 26.

For example, in column 1 the sum of all the numbers is 26 and we obtain 0 by reducing 26 in mod 26. Let R(i) be the value obtained by reducing a the ith column sum to mod 26, then we must have:

i   S(i)
1    0
2    0
3    13
4    15
5    4
6    21
7    12
8    1
9    18
10   0
11   1
12   18
13   9
14   20
15   8
16   13
17   5
18   20
19   9
20   3
21   0
22   0
23   0

Placing the addition results side by side we have:

0 0 13 15 4 21 12 1 18 0 1 18 9 20 8 13 5 20 9 3 0 0 0

Now, removing the 0's we have:

13 15 4 21 12 1 18 1 18 9 20 8 13 5 20 9 3

We now denote the letters by their respective positions in the alphabet. Thus, 1=a, 2=b, 3=c, ...., 25=y, and obtain "MODULAR ARITHMETIC" as the required decoded message.

Edited on April 3, 2008, 1:33 pm
 Posted by K Sengupta on 2008-04-03 13:27:47

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