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 I loved (Posted on 2013-06-05)
Live Devo love devil.
The above sentence of 4 words is a palindromic alphametics, using only various subsets of " I loved" letters and boasting a unique solution.
Live + Devo + love = devil.
Decoding it analytically is not an easy task.

Btw Devo was a punk group, famous in the seventies.

Source: I've found this sequence in an essay by jjnlm, the comments are mine.

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 A devilish problem (spoiler) | Comment 1 of 3
```Well, let's start at the left-hand side.

a) The carryover from adding three numbers is 0, 1 or 2.
Thus, D is clearly 1 or 2.

b) Looking at the last column, we observe that E cannot be 0

c) Looking at the first two columns, we see that
2L + D + carryover = 10D + E

Rearranging, L = (9D + E - Carryover)/2
Possibly values are

D  E  carryover L
-- -- --------- --
2  1  1         9
2  2  2         9 -- no good D and E are the same

1  1  2         4 -- no good D and E are the same
1  1  0         5 -- no good D and E are the same
1  2  1         5
1  3  2         5
1  3  0         6
1  4  1         6
1  5  2         6
1  5  0         7
1  6  1         7
1  7  2         7  -- no good E and L are the same
1  7  0         8
1  8  1         8  -- no good E and L are the same
1  9  2         8
1  9  0         9  -- no good E and L are the same

d) Looking at the last column, we see that O = L - 2E (mod 10)

Possible values are

D  E  L  O
-- -- -- --
2  1  9  7
1  2  5  1 -- no good O and D are the same
1  3  5  9
1  3  6  0
1  4  6  8
1  5  6  6 -- no good O and L are the same
1  5  7  7 -- no good O and L are the same
1  6  7  8
1  7  8  9
1  9  8  7

e) Do the sum mod 9, we determine that

L + 2O +2E + 2V = 0 (mod 9),
ie,
L + 2O +2E + 2V = 0

Possible values are

D  E  L  O  V
-- -- -- -- --
2  1  9  7  1 -- no good V and E are the same
1  3  5  9  8
1  3  6  0  3 -- no good V and E are the same
1  4  6  8  3
1  6  7  8  5
1  7  8  9  7 -- no good V and E are the same
1  9  8  7  7 -- no good V and L are the same

f) Looking at the last two columns, we see that
I = 3V + carryover from 2E + O (all mod 10)

Possible values are:

D  E  L  O  V  I
-- -- -- -- -- --
1  3  5  9  8  5 -- no good I and L are the same
1  4  6  8  3  0
1  6  7  8  5  7 -- no good I and L are the same

So the only solution is

D  E  L  O  V  I
-- -- -- -- -- --
1  4  6  8  3  0

6034
1438
6834
----
14306
```

 Posted by Steve Herman on 2013-06-06 12:14:35

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