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

(In reply to

answer by K Sengupta)

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**