The following puzzle has a spelling mistake: DOUCE should be DOUZE.
The correct version is: French alphametic (corrected)
(Surprisingly the faulty version allows feasible solutions.)
Every letter stands for a digit in base-10 representation, different letters stand for different digits:
UN
UN
DEUX
+ DOUCE
------------
SEIZE
Which digit does each letter represent?
(Please present the full analysis how these digits can be determined.)
Answer
sorry for the format I don't know how to put spoiler to multiple lines of formula. I am just putting spoiler to the answer below.
remaining numbers : 0-1-2-3-4-5-6-7-8-9
UN
UN
DEUX
+ DOUCE
-------
SEIZE
Giving 0 to E , and since we know S = D + 1 I random them as 8 - 9. I will try giving 2 to O . This is what we have:
E=0 , D=8 , S=9, O=2, remaining numbers : 1-3-4-5-6-7
UN
UN
80UX
+ 82UC0
-------
90IZ0
Now we know that :
N+N+X = 10 or 20
U+U+U+C + B = Z where B = 1 or 2
U + 0 = I but we know they can't be the same so there is a remainder which means:
U + W = I where W = 1 or 2
N N X possibilities:
a1: 7+7+6
a2: 3+3+4
a3: 2+2+6
To determine whether if W or B can be 1 or 2 I pick a2 to give big numbers to net stage and I get;
E=0 , D=8 , S=9, O=2, N=3, X=4, remaining numbers : 1-5-6-7
U3
U3
80U4
+ 82UC0
-------
90IZ0
U+U+U+C + 1 = Z
U + W = I where W = 1 or 2
U can be 5 or 6, and I can 6 or 7 because of remaining numbers.
UUUC possibilities:
6661 +1 = 20 x Z can't be 0
6665 +1 = 24 x Z can't be 4
5557 +1 = 23 x Z can't be 3
5551 +1 = 17 so let's give our values and rewrite:
ANSWER:
E=0 , D=8 , S=9, O=2, N=3, X=4, U=5, C=1, Z=7, I=6
53
53
8054
+ 82510
-------
90670
Is my solution but I am sure there are more possibilities and this is not a unique solution because of many possibilities.
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