diff --git a/src/constraint_solver/constraint_solver.h b/src/constraint_solver/constraint_solver.h
index 36ada815e4..3c51028267 100644
--- a/src/constraint_solver/constraint_solver.h
+++ b/src/constraint_solver/constraint_solver.h
@@ -3738,6 +3738,10 @@ class IntVar : public IntExpr {
   // Accepts the given visitor.
   virtual void Accept(ModelVisitor* const visitor) const;
 
+  // IsEqual
+  virtual IntVar* IsEqual(int64 constant) = 0;
+  virtual IntVar* IsDifferent(int64 constant) = 0;
+
  private:
   DISALLOW_COPY_AND_ASSIGN(IntVar);
 };
diff --git a/src/constraint_solver/expressions.cc b/src/constraint_solver/expressions.cc
index 0888b4f962..4fd39142f3 100644
--- a/src/constraint_solver/expressions.cc
+++ b/src/constraint_solver/expressions.cc
@@ -301,6 +301,14 @@ class DomainIntVar : public IntVar {
     }
   }
 
+  virtual IntVar* IsEqual(int64 constant) {
+    return NULL; // IMPLEMENT ME.
+  }
+
+  virtual IntVar* IsDifferent(int64 constant) {
+    return NULL;  // IMPLEMENT ME
+  }
+
   void Process();
   void Push();
   void ClearInProcess();
@@ -1342,6 +1350,28 @@ class BooleanVar : public IntVar {
   virtual string DebugString() const;
   virtual int VarType() const { return BOOLEAN_VAR; }
 
+  virtual IntVar* IsEqual(int64 constant) {
+    if (constant > 1 || constant < 0) {
+      return solver()->MakeIntConst(0);
+    }
+    if (constant == 1) {
+      return this;
+    } else { // constant == 0.
+      return solver()->MakeDifference(1, this)->Var();
+    }
+  }
+
+  virtual IntVar* IsDifferent(int64 constant) {
+    if (constant > 1 || constant < 0) {
+      return solver()->MakeIntConst(1);
+    }
+    if (constant == 1) {
+      return solver()->MakeDifference(1, this)->Var();
+    } else { // constant == 0.
+      return this;
+    }
+  }
+
   void RestoreValue() { value_ = kUnboundBooleanVarValue; }
 
   virtual string BaseName() const { return "BooleanVar"; }
@@ -1524,6 +1554,22 @@ class IntConst : public IntVar {
   virtual string DebugString() const;
   virtual int VarType() const { return CONST_VAR; }
 
+  virtual IntVar* IsEqual(int64 constant) {
+    if (constant == value_) {
+      return solver()->MakeIntConst(1);
+    } else {
+      return solver()->MakeIntConst(0);
+    }
+  }
+
+  virtual IntVar* IsDifferent(int64 constant) {
+    if (constant == value_) {
+      return solver()->MakeIntConst(0);
+    } else {
+      return solver()->MakeIntConst(1);
+    }
+  }
+
  private:
   int64 value_;
 };
@@ -1602,6 +1648,14 @@ class PlusCstIntVar : public IntVar {
                                   var_);
   }
 
+  virtual IntVar* IsEqual(int64 constant) {
+    return var_->IsEqual(constant - cst_);
+  }
+
+  virtual IntVar* IsDifferent(int64 constant) {
+    return var_->IsDifferent(constant - cst_);
+  }
+
  private:
   IntVar* const var_;
   const int64 cst_;
@@ -1739,6 +1793,14 @@ class PlusCstDomainIntVar : public IntVar {
                                   var_);
   }
 
+  virtual IntVar* IsEqual(int64 constant) {
+    return var_->IsEqual(constant - cst_);
+  }
+
+  virtual IntVar* IsDifferent(int64 constant) {
+    return var_->IsDifferent(constant - cst_);
+  }
+
  private:
   DomainIntVar* const var_;
   const int64 cst_;
@@ -1878,6 +1940,14 @@ class SubCstIntVar : public IntVar {
                                   var_);
   }
 
+  virtual IntVar* IsEqual(int64 constant) {
+    return var_->IsEqual(cst_ - constant);
+  }
+
+  virtual IntVar* IsDifferent(int64 constant) {
+    return var_->IsDifferent(cst_ - constant);
+  }
+
  private:
   IntVar* const var_;
   const int64 cst_;
@@ -2009,6 +2079,14 @@ class OppIntVar : public IntVar {
                                   var_);
   }
 
+  virtual IntVar* IsEqual(int64 constant) {
+    return var_->IsEqual(-constant);
+  }
+
+  virtual IntVar* IsDifferent(int64 constant) {
+    return var_->IsDifferent(-constant);
+  }
+
  private:
   IntVar* const var_;
 };
@@ -2162,6 +2240,22 @@ class TimesPosCstIntVar : public IntVar {
                                   var_);
   }
 
+  virtual IntVar* IsEqual(int64 constant) {
+    if (constant % cst_ == 0) {
+      return var_->IsEqual(constant / cst_);
+    } else {
+      return solver()->MakeIntConst(0);
+    }
+  }
+
+  virtual IntVar* IsDifferent(int64 constant) {
+    if (constant % cst_ == 0) {
+      return var_->IsDifferent(constant / cst_);
+    } else {
+      return solver()->MakeIntConst(1);
+    }
+  }
+
  private:
   IntVar* const var_;
   const int64 cst_;
@@ -2315,6 +2409,22 @@ class TimesPosCstBoolVar : public IntVar {
                                   var_);
   }
 
+  virtual IntVar* IsEqual(int64 constant) {
+    if (constant % cst_ == 0) {
+      return var_->IsEqual(constant / cst_);
+    } else {
+      return solver()->MakeIntConst(0);
+    }
+  }
+
+  virtual IntVar* IsDifferent(int64 constant) {
+    if (constant % cst_ == 0) {
+      return var_->IsDifferent(constant / cst_);
+    } else {
+      return solver()->MakeIntConst(1);
+    }
+  }
+
  private:
   BooleanVar* const var_;
   const int64 cst_;