Farmer Jeb usually plants his own crops; this year he’s paying you to plant them. However, he wants them planted very particular; and instead of just plain telling you where to plant what. He gives you a list of the foods and some clues.

Foods (in no particular order): wheat, peas, carrots, potatoes, tomatoes, and onions.

Clues:(some are these are tricky, but funny)

  1. The “toes” don’t touch
  2. Wheat is not next to the carrots
  3. Onion sandwich
  4. The pea’s are either to the direct left or the direct right of the middle food
  5. The potatoes are to the direct left of the onions

  6. Wheat is at one of the ends

  7. Potatoes can not be next to the peas

  8. Between the pea’s and wheat there is Tomatoes

  9. The pea’s don’t touch the carrots

  10. Potatoes come after the carrots

Can you figure out where to plant which crop?

  • $\begingroup$ Are we supposed to assume that exactly one of each is planted? If so, what is "the middle food" meant to mean? (There are six things listed here.) $\endgroup$
    – Gareth McCaughan
    Nov 20 '17 at 13:25
  • $\begingroup$ @Gareth Don't think that's possible. There has to be multiple of them(maybe 2. Notice the plural?) but only one wheat crop so that we get an odd number... $\endgroup$
    – Sid
    Nov 20 '17 at 13:30
  • $\begingroup$ It seems to me like if we're allowed multiple instances then there will be lots of solutions. I think this question needs clarifying. $\endgroup$
    – Gareth McCaughan
    Nov 20 '17 at 13:31
  • $\begingroup$ What is the layout of the fields? $\endgroup$ Nov 20 '17 at 13:37
  • 3
    $\begingroup$ @Gareth, I think that if we have to assume anything it's a flaw in the question. $\endgroup$ Nov 20 '17 at 13:40

Here's the answer:

The order from left to right is: " Carrots, Potatoes, Onions, Peas, Tomatoes, Wheat"


From No. 6, we know that Wheat is at one of the ends.
(W) _ _ _ _ (W)
From 5,9 and 4, we get that Wheat can only be at the right-most end.
_ _ _ _ Wheat
Fitting in Tomatoes and Peas from no. 8, we get the half of the field ready.
_ _ _ Pea Tomato Wheat
Then, From Clue 9, 5 and 10, we fit in the rest of the vegetables.
Carrot Potato Onion Pea Tomato Wheat.


This ordering seems to fit all the conditions, in so far as I understand them (the question seems deliberately vague):

carrots potatoes onions peas tomatoes wheat


Peas aren't next to potatoes (#7), carrots (#9) or wheat (#8). So if they aren't at the end then they are next to onions and tomatoes. Using #5 this gives us: potatoes onions peas tomatoes. The remaining two things, carrots and wheat, can't be next to one another (#2) so one is at each end; and #10 says carrots are at the left rather than the right. This gives the ordering above.

There remains only the possibility that

peas are at one end. But that is inconsistent with #4.

Dubious interpretations:

"Onion sandwich" seems just to mean that onions aren't at the end. Perhaps "to the direct left or the direct right of the middle food" actually means "to the direct left or right of the middle".


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