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    <p>While Martin Smith's solution does not entirely solve this problem, it did inspire me to look into using CTEs and I think I got it.</p> <p>Once I realized every 3 ingredient combination is really 2 different 2 ingredient combinations that share 1 common ingredient, I decided to find all 2 ingredient combinations and then find every combination of those that have at least 1 ingredient in common and both have effects that the other does not have.</p> <p>Then check to make sure every 3 ingredient combination has no poison effects (I already know each individual 2 ingredient combination has no poison effects, but just because A+B has no poison and B+C has no poison doesn't mean A+B+C won't have poison. It's possible that combing A with C will produce a poison effect).</p> <p>Then I join all 3 ingredients back to the Effect table to display which effects are produced with each combination.</p> <p>This query has a 3 minute 50 second execution time on my system. That's not cool. But at least I am getting the results I want now.</p> <pre><code>WITH Combination AS ( --Finds all 2 ingredient combinations that have shared effects that are not poisons select ROW_NUMBER() OVER (ORDER BY i1.Name, i2.Name) UniqCombination, i1.UniqIngredient UniqIngredient1, i2.UniqIngredient UniqIngredient2, COUNT(1) NumberOfEffects from Ingredient i1 cross join Ingredient i2 INNER JOIN IngredientEffectJT jt1 ON i1.UniqIngredient = jt1.UniqIngredient INNER JOIN IngredientEffectJT jt2 ON i2.UniqIngredient = jt2.UniqIngredient INNER JOIN Effect e ON jt1.UniqEffect = e.UniqEffect AND jt2.UniqEffect = e.UniqEffect WHERE i1.UniqIngredient &lt; i2.UniqIngredient GROUP BY i1.UniqIngredient, i1.name, i2.UniqIngredient, i2.Name HAVING SUM(e.poison) = 0 ), Potion AS ( --Matches up all 2 ingredient combinations in the Combination CTE with the effects for that combination SELECT DISTINCT c.UniqCombination, c.UniqIngredient1, i1.Name Ingredient1, c.UniqIngredient2, i2.Name Ingredient2, e.UniqEffect, e.Name Effect FROM Combination c INNER JOIN Ingredient i1 ON c.UniqIngredient1 = i1.UniqIngredient INNER JOIN Ingredient i2 ON c.UniqIngredient2 = i2.UniqIngredient INNER JOIN IngredientEffectJT jt1 ON c.UniqIngredient1 = jt1.UniqIngredient INNER JOIN IngredientEffectJT jt2 ON c.UniqIngredient2 = jt2.UniqIngredient INNER JOIN Effect e ON jt1.UniqEffect = e.UniqEffect AND jt2.UniqEffect = e.UniqEffect ), BigCombination AS ( --Matches 2 combinations together where 1 ingredient is the same in both combinations. SELECT c1.UniqIngredient1, CASE WHEN c1.UniqIngredient1 = c2.UniqIngredient1 THEN c1.UniqIngredient2 ELSE c2.UniqIngredient1 END UniqIngredient2, c2.UniqIngredient2 UniqIngredient3 FROM Combination c1 INNER JOIN Combination c2 ON (c1.UniqIngredient1 = c2.UniqIngredient1 OR c1.UniqIngredient2 = c2.UniqIngredient1 OR c1.UniqIngredient2 = c2.UniqIngredient2) AND c1.UniqCombination &lt; c2.UniqCombination --This WHERE clause sucks because there are 2 different select queries that must run twice each. --They have to run twice because I have to EXCEPT 1 from 2 and 2 from 1 to make sure both combinations are contributing something new. WHERE EXISTS( SELECT p1.UniqEffect FROM Potion p1 WHERE p1.UniqCombination = c1.UniqCombination EXCEPT SELECT p2.UniqEffect FROM Potion p2 WHERE p2.UniqCombination = c2.UniqCombination) AND EXISTS( SELECT p2.UniqEffect FROM Potion p2 WHERE p2.UniqCombination = c2.UniqCombination EXCEPT SELECT p1.UniqEffect FROM Potion p1 WHERE p1.UniqCombination = c1.UniqCombination) ), BigPotionCombination AS ( --Combinations were made only from other combinations that made potions, but it's possible the new --ingredients mixing together could create a new poison effect. This will remove combinations that create new poison effects SELECT DISTINCT c.* FROM BigCombination c INNER JOIN IngredientEffectJT jt1 ON c.UniqIngredient1 = jt1.UniqIngredient INNER JOIN IngredientEffectJT jt2 ON c.UniqIngredient2 = jt2.UniqIngredient INNER JOIN IngredientEffectJT jt3 ON c.UniqIngredient3 = jt3.UniqIngredient INNER JOIN Effect e ON (jt1.UniqEffect = e.UniqEffect AND (jt2.UniqEffect = e.UniqEffect OR jt3.UniqEffect = e.UniqEffect)) OR (jt2.UniqEffect = e.UniqEffect AND jt3.UniqEffect = e.UniqEffect) GROUP BY c.UniqIngredient1, c.UniqIngredient2, c.UniqIngredient3 HAVING SUM(e.Poison) = 0 ) --Combinations have to be joined back to Effect again to display the effects that the potions have. SELECT DISTINCT i1.Name Ingredient1, i2.Name Ingredient2, i3.Name Ingredient3, e.Name Effect FROM BigPotionCombination c INNER JOIN Ingredient i1 ON c.UniqIngredient1 = i1.UniqIngredient INNER JOIN Ingredient i2 ON c.UniqIngredient2 = i2.UniqIngredient INNER JOIN Ingredient i3 ON c.UniqIngredient3 = i3.UniqIngredient INNER JOIN IngredientEffectJT jt1 ON c.UniqIngredient1 = jt1.UniqIngredient INNER JOIN IngredientEffectJT jt2 ON c.UniqIngredient2 = jt2.UniqIngredient INNER JOIN IngredientEffectJT jt3 ON c.UniqIngredient3 = jt3.UniqIngredient INNER JOIN Effect e ON (jt1.UniqEffect = e.UniqEffect AND (jt2.UniqEffect = e.UniqEffect OR jt3.UniqEffect = e.UniqEffect)) OR (jt2.UniqEffect = e.UniqEffect AND jt3.UniqEffect = e.UniqEffect) ORDER BY Ingredient1, Ingredient2, Ingredient3, Effect </code></pre>
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