After twenty-five years of thinking about this problem I decided to
write a web page about it. Here is the problem:
Can you find three foods such that all three do not go
(by any reasonable definition of foods "going together") but every pair
them does go together?
There are many ways to interpret this "going together" but an example
would be three pizza toppings---A, B, and C---such that a pizza with A
B is good, and a pizza with A and C is good, and a pizza with B and C
good, but a pizza with A, B, and C is bad. Or you might find three
spices or other ingredients which do not go together in some recipe yet
pair of them is fine.
Alternatively, you could try for an impossibility proof---to
logically that whenever all three pairs are OK then the triple must be
But I think that would be difficult to show because there are
of chemical processes which require three ingredients for a reaction
no two react. So, to the extent that cooking is chemistry, it seems
one can not rule out an incompatible triad a priori
I learned of The Incompatible Food Triad
from the philosopher Nuel Belnap when I was a graduate student in the
1970's. He mentioned it in discussion while we were at a dinner
In the intervening years, I have occasionally passed it on it at
dinners to my colleagues and graduate students, always without success.
(at a wonderful dinner in southern Spain with a colleague, two graduate
and a vast platter of tentacles and mysterious seafood,) I realized it
been twenty-five years with zero progress. It was time to start getting
about finding a solution! First, a Google search found no references at
Three billion web pages, and none discuss the question. Then I
Prof. Belnap to see if he had found a solution in the intervening
He tells me that has made no progress either. He also informed me that
learned the problem from the philosopher Wilfrid Sellars over a dinner,
that he suspects Sellars is the originator but can not be sure.
Feeling that better minds (or taste buds) than mine must now be brought
bear in this research, I decided to write this web page in August
2003. It is hard to believe that there are any such pressing questions
left about which one
can write the first web page on the internet.
If you think you have a solution to The Incompatible Food Triad
that all three pairs are compatible. Always (so far)
people think they have a solution, it turns out that they didn't check
of the pairs, and that the incompatibility of the triad can be found to
in the incompatibility of one of the three pairs. Then, if you are
confident of your answer, please send
and I will collate the answers and report progress below. (YOU could
get famous, right here!!!)
solutions may be idiosyncratic,
with different eaters having different opinions about taste
so there may be some discussion to follow.
Also, if you find any other discussion of the problem (in print, on a
web page, or wherever) please let me know.
Not a solution, but Craig Westerland (at the
University of Michigan) responds to the question with a complementary
question: Are there three foods which you would eat together, but
you wouldn't eat any pair without the third?
"Luka" suggests that the tea + milk + lemon juice
triad, famously described by Richard Feynman in his autobiographical Surely
is a solution. I have discussed this
triad many times over the years. Most agree that this is not a solution
because lemon+milk is a very bad pair. It forms curdles and that is the
source of the problem with the triad, which is the point of the Feynman
story. However Luka points out that milk+lemon juice is a step in a
recipe for what is called "panir" or "paneer" or "queso blanco" or
"farmer's cheese". You then strain it in cheese cloth, and press it
until it is firm like tofu. My reaction is that if you like this kind
of bland cheese and you like milk in your tea, then you would probably
like a tea-flavored cheese. I can't test this because I don't like milk
in my tea, but someone who does and who also likes to make panir should
let us know if a tea-flavored panir is good or bad.
Moses Liskov follows up on this with a suggestion
for a cheese that would taste worse:
If you buy the paneer argument, then I think espresso + milk + lemon juice qualifies as a triad. Espresso + milk is clearly popular.. and Italians often have espresso with lemon. However, even if tea-flavored cheese might be pleasant, espresso-flavored cheese is a gross concept: paneer is a light, delicate cheese, and I've never had a cheese with a strong non-cheese flavor that I liked (except for hotness, as in pepperjack).
Heidi Shook makes a suggestion but also shoots it
...potatoes, mayonnaise, and cabbage. Recipes often contain two out of the three, but not all three ingredients. Potatoes & mayo for a potato salad, cabbage & mayo for a coleslaw, and potatoes & cabbage for a veggie side are common, but mixing all three is rare.
I did find two exceptions on google--corned beef, cabbage and potatoes can be served with a horseradish sauce on the side. I'm not a corned beef eater, but I am guessing the sauce is for the meat. Anyway, the sauce sometimes contains mayonnaise and the recipes aren't specific about which foods get sauce treatment. The other exception is somebody has come up with a corned beef salad that actually contains all three ingredients mixed together. That recipe doesn't seem to be widely known, leaving me to think it must taste as terrible as it sounds to me.
Joanne Murray at first suggests the following:
chocolate, chicken and honey
there's honey-butter chicken (yummy)
chicken with mole (chocolate) sauce (mexican)
and all kinds of sweets with chocolate-honey sauce
but chocolate-honey-chicken sounds revolting. google supports this. you can find many recipes for "honey chicken" "chocolate honey" and "mole chicken" but nothing whatever for "chocolate honey chicken" "honey chocolate chicken" "honey mole chicken" or "mole honey chicken".
But then she found a counter-example and sent me this:
oh well, sorry to bother you with a loser. (though i still say chocolate-honey-chicken sounds disgusting to me).
Vincent Tsoi suggests "Chocolate, Strawberry,
Milkshake" but I disagree, having made end enjoyed milk shakes from
vanilla, chocolate and strawberry mixed together.
Carolyn Williams apparently feels there is no
solution (for her) as she comments "Get pregnant, and you can eat
Gwen Fisher suggests:
a. Salted cucumbers
a and b in sweet pickles
a and c in tzaziki (sp?), the greek yogurt dish.
b and c is common.
a, b,and c together is pretty gross. I was trying to make tzaziki once, and
accidentally used sweetened vanilla yogurt. I had to throw it out. Yuck.
I can't comment on this, as I draw the line at a+c.
Joshua Harwood suggests a solution with mixed
A = gin
B = tonic water
C = orange guice
A+B goes together. (Gin & tonic.)
B+C goes together. (Orange fizzer, prom date punch.)
C+A goes together. (Gin & juice.)
A+B+C does not go together. (Wretched surprise!)
I'll have to do an experiment, since I don't see what the surprising
problem might be.
Melinda Green suggests lemon-cocoa-curry:
lemon-cocoa = chocolate covered candied lemon rinds
cocoa-curry = mole,
lemon-curry = thai
Can there not be a lemon mole?
. . .
<It turns out this page started
generating far more mail than I could keep up with, so I quickly
stopped adding posts.>
One critical email I received may deserve printing:
That this thought experiment merits a
web page is really quite
astounding. That I decided to write you an e-mail telling you
even more astounding. And that I don't drink myself stupid
this exchange will be the most astounding non-event in the history of
mankind. I am baffled, shattered, and destroyed by the
pointlessness of The Incompatible Food Triad experiment. It makes
ill. I promise you, sir, I will never again be the same after
witnessing the sheer mind-blowing uselessness of that puzzle. My
as I know it, is over. I once was lost, but then I was found, and
I found your website linked to Wikipedia and now I am lost again,
irretrievably lost in a dark maze, a pitch dark maze with the Minotaur
of Bafflement hunting me down. I shall not escape him, I shall
escape my doom. No, good sir, instead I fall - far and away, even
myself I fall until I slam forcefully into the cold steel floor of my
own mind, crippled and alone, dead to all sensation. I am gone,
and I shall never return.
Quantitative Algorithmic Approach:
I asked some folks at Google if they could automate the question by
selecting a set of food words, enumerating all pairs and triples of
them, then searching within recipe pages and tabulating the page counts
of foods, looking for a triple with the correct property.
But it was apparently too much of a challenge even for Google to
determine what words are foods and what pages are recipes.
I love the answer by Noah Snyder and his colleagues at U.C. Berkeley,
who suggest these three items: a shot of tequila, a shot of
tequila, a shot of tequila.
In January, 2010, I received this authoratative comment from Hervé
of the AgroParisTech
him, see This's
. I will present it here as perhaps my final word on the
Dear George Hart,
May I tell you that your question is wrong, and this is why there is no
Indeed, there is a myth called "food pairing", but it is not scientific, as
food appreciation is a question of art... and art always espapes (aesthetics)
Moreover, think of Munster Cheese, durian fruits, hot brain of apes in
skulls... If someone had it when young, it's good!
Finally, an anecdote: I asked once to my friend Pierre Gagnaire if he would
be able to mix the impossible pair camembert cheese+raspberries... and he
did it at once. The recipe is in my book "Cooking, a quintessential art", at
California University Press. Moreover, in this case, you need absolutely a
poor camembert to get a "good" result. A discussion is given also in the
final chapter of my book "Building a meal" (Columbia University Press)
Directeur scientifique de la Fondation Science & Culture Alimentaire
(Académie des sciences)
Membre correspondant de l'Académie d'agriculture de France
Membre associé de l'Académie royale des sciences, des arts et des lettres de
Président du Comité Pédagogique des Hautes Etudes du Goût
Conseiller Scientifique de la revue Pour la Science
Groupe de Gastronomie Moléculaire
Laboratoire de Chimie, AgroParisTech