A scip model for solving the puzzle at https://www.puzzleprime.com/brain-teasers/deduction/send-more-money/

send-more-money.zpl

# A scip model for solving the puzzle at
# https://www.puzzleprime.com/brain-teasers/deduction/send-more-money/
       
set letters  := { 'D', 'E', 'M', 'N', 'O', 'R', 'S', 'Y' };

# what digit does each letter represent?
var digits[letters] integer >=0 <=9;

# all digits must be different
subto d: forall <l1,l2> in letters*letters with l1 > l2 do
	abs(digits[l1] - digits[l2]) >= 1;

# the leftmost digit cannot be zero
subto d1: digits['S'] >= 1;
subto d2: digits['M'] >= 1;

# the three numbers behind the words
var number_1 ; var number_2 ; var number_3 ;

subto f1: number_1 ==
	digits['S']*1000 + digits['E']*100 + digits['N']*10 + digits['D']*1;
subto f2: number_2 ==
	digits['M']*1000 + digits['O']*100 + digits['R']*10 + digits['E']*1;
subto f3: number_3 ==
	digits['M']*10000 + digits['O']*1000 + digits['N']*100 + digits['E']*10 + digits['Y']*1;


subto total: number_1 + number_2 == number_3;