Transcript Document 7692128

gerald
+donald
--------robert
---------
Variables
geraldonbt
gerald
+donald
--------robert
---------
Domains
value in range [0..9]
Observations
g can’t be zero
These are unary constraints
d can’t be zero
r can’t be zero
t is even (observation due to Christine)
All variables take different values
binary constraints?
gerald
+donald
--------robert
--------d + 10.l + 100.a + 1000.r + 10000.e + 100000.g
+
d + 10.l + 100.a + 1000.n + 10000.o + 100000.d
=
t + 10.r + 100.e + 1000.b + 10000.o + 100000.r
d + 10.l + 100.a + 1000.r + 10000.e + 100000.g
+
d + 10.l + 100.a + 1000.n + 10000.o + 100000.d
gerald
+donald
--------robert
---------
=
t + 10.r + 100.e + 1000.b + 10000.o + 100000.r
Introduce carries
t + 10.carry1 = 2.d
r + 10.carry2 = l + l + carry1
e + 10.carry3 = a + a + carry2
b + 10.carry4 = r + n + carry3
o + 10.carry5 = e + o + carry4
r = g + d + carry5
Observations
g can’t be zero
d can’t be zero
r can’t be zero
t is even (observation due to Christine)
[gerald() : Problem
-> let p := makeProblem("CRYPT-ARITHMETIC: gerald + donald = robert",13),
g := makeIntVar(p,"g",0 ,9),
e := makeIntVar(p,"e",0 ,9),
r := makeIntVar(p,"r",0 ,9),
a := makeIntVar(p,"a",0 ,9),
l := makeIntVar(p,"l",0 ,9),
d := makeIntVar(p,"d",0, 9),
o := makeIntVar(p,"o",0 ,9),
n := makeIntVar(p,"n",0 ,9),
b := makeIntVar(p,"b",0 ,9),
t := makeIntVar(p,"t",0, 9),
letters := set(g,e,r,a,l,d,o,n,b,t),
word1 := makeBoundIntVar(p,"gerald",0,999999),
word2 := makeBoundIntVar(p,"donald",0,999999),
word3 := makeBoundIntVar(p,"robert",0,999999)
in (for i in (1 .. 9)
for j in (i + 1 .. 10)
post(p,letters[i] !== letters[j]),
post(p, list(100000,10000,1000,100,10,1) scalar list(g,e,r,a,l,d) == word1),
post(p, list(100000,10000,1000,100,10,1) scalar list(d,o,n,a,l,d) == word2),
post(p, list(100000,10000,1000,100,10,1) scalar list(r,o,b,e,r,t) == word3),
post(p, word1 + word2 == word3),
p)]