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Here is a short puzzle I made:

There are 10 people arranged in a row, and each of them has a friend and an enemy also present in the row. Your goal is to identify the friend and enemy of each person.

Friends:

A friend relation is two-sided, that is, if (1)'s friend is (2), then (2)'s friend must be (1).

Enemies:

An enemy relation is one-sided, that is, if (1)'s enemy is (2), then (2)'s enemy can be any other person, maybe (1).

Extra Facts about friends and enemies:

  • No two people can have the same friend or the same enemy.
  • The friend and enemy of a person must be two distinct people.
  • A person cannot be the enemy or friend of themselves.

Directions:

  • 'R': Both the friend and the enemy are to the right of that person.
  • 'L': Both the friend and the enemy are to the left of that person.
  • 'O': The friend and the enemy are in opposite sides of that person.
    It is not given which one is to the left and which one is to the right.

The Puzzle:

PERSON A B C D E F G H I J
DIRECTIONS R O L O L O R R O L
FRIENDS
ENEMIES

Extra Information required to guarantee a unique solution:

It is also known that A's enemy is not E.

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  • $\begingroup$ Is A right of B or B right of A? $\endgroup$
    – Helena
    Jan 31, 2023 at 21:48
  • $\begingroup$ Oh B is to the right of A, I didn't see the need to clarify that as it is known the friend and enemy are to the right of A. $\endgroup$ Feb 1, 2023 at 1:19
  • $\begingroup$ Now that you say it, that is indeed obvious. $\endgroup$
    – Helena
    Feb 1, 2023 at 19:00

1 Answer 1

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H and I both must be related to J because there is nothing further right. So either I-J is a friend pair or H-J is a friend pair.
G's friends and enemies both must be between H, I, J. But the friend cannot be H. It cannot be J either because of previous point so G's friend is I. We got 2 friend pairs G-I and H-J.
So H's enemy must be I and I's enemy must be J. enter image description here

This means G's enemy must be H. F's friend cannot be in the right side so their enemy must be. So F's enemy is G.
C and B are both related to A as nothing is further left. Suppose if C's friend was B, then C's enemy must be A. But then B's enemy must be to the left of them which means B's enemy is also A therefore a contradiction.
This gives us A-C as friend pair, C's enemy as B and B's enemy as A. enter image description here

E and F are not friends. So neither are D and B which means D's friend is to the right and enemy is to the left. Therefore D's enemy is C.
Suppose E's friend was D. Then there wouldnt be a valid enemy for E. Which means E's friend is B and D's friend is F. enter image description here

Now E's enemy must be D. A's enemy cannot be E (mentioned in problem) so it is F. And J's enemy is E.
enter image description here

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