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Incompatible Food Triad
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The Incompatible Food Triad is a puzzle to find three foods for which any pair will taste good together, but all three together will not. The puzzle is believed to have originated with the philosopher Wilfrid Sellars, and has been spread by some of his former colleagues and students, including Nuel Belnap and George W. Hart. The puzzle was also featured on WNYC's The Brian Lehrer Show False solutions Given three foods that don't go together, it's usually because two of them don't go together. For example, Richard Feynman's famous example of accidentally requesting milk and lemon in his tea is not a solution. While tea and lemon do go together, and tea and milk do go together, milk and lemon do not go together. For this solution to work, milk and lemon would have to go together as well. According to Hart, most attempted solutions tend to overlook one of the three pairs. Issues of personal taste and preparation complicate the issue, as combinations some consider acceptable sound unpalatable to others, and problems such as milk curdling with the addition of lemon juice can potentially be overcome if a cheesemaking process is employed. Formula Find a counter example to either of the following (equivalent) putative implications, (where R(x,y,...) means "x, y, ... all go together") : #Given any three foods A, B, and C, if [R(A,B), R(A,C) and R(B,C)] then R(A,B,C) #Given any three foods A, B, and C, if ~R(A,B,C) then [~R(A,B) or ~R(A,C) or ~R(B,C)]. Possible solutions In a posting on its website after the puzzle was aired on the WNYC radio show in New York, Beer, 7Up, and Whiskey was given as an examples with the statement that beer with 7Up makes shandy), beer with whiskey makes a boilermaker and whiskey with 7Up is a 7 & 7, but the three together would "make you sick". Other possible solution from viewers included: * pie crust, raspberries and spinach *chocolate, peanut butter and chicken A few of the "classic" solutions are: #Salted cucumbers, sugar, yogurt. #Orange juice, gin, tonic. #Lemon, cocoa, curry. 
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