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gerald +donald --------- robert ---------

gerald +donald --------- robert ---------. gerald +donald --------- robert ---------. Variables g e r a l d o n b t. Domains value in range [0..9]. Observations g can’t be zero d can’t be zero r can’t be zero t is even (observation due to Christine).

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gerald +donald --------- robert ---------

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  1. gerald +donald --------- robert ---------

  2. gerald +donald --------- robert --------- Variables g e r a l d o n b t Domains value in range [0..9] Observations g can’t be zero d can’t be zero r can’t be zero t is even (observation due to Christine) These are unary constraints All variables take different values binary constraints?

  3. 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

  4. 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 gerald +donald --------- robert --------- Observations g can’t be zero d can’t be zero r can’t be zero t is even (observation due to Christine) 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

  5. [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)]

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