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## Love Island

Logic puzzles require you to think. You will have to be logical in your reasoning.

 Puzzle ID: #46839 Fun: (2.67) Difficulty: (2.69) Category: Logic Submitted By: griphook

Four men and four women are in Love Island. Each one falls in love with another and is himself/herself loved by someone else in a complete 8 person loop.

Peter falls in love with a girl who is unfortunately in love with Albert. Joseph loves a girl who loves the man who loves Elaine. Liza is loved by the guy who is loved by the girl who is loved by Paolo. Linda hates Paolo and is hated by the man whom Amy loves.

No guy/guy or girl/girl in Love Island.

Who loves Joseph and whom does Joseph love?

Linda loves Joseph, and Joseph loves Amy.

An 8 person loop may be represented as follows:

M1 > G1 > M2 > G2 > M3 > G3 > M4 > G4 >

From second paragraph:

Line 1: Peter > G > Albert > G >
Line 2: Joseph > G > M > Elaine >
Line 3: Paolo > G > M > Liza >
Line 4: Linda hates Paolo and is hated by the man Amy loves.

Step One: Assume Peter is M1. (Peter can be M2 or M3 or M4 with the same result.)

Peter > G1 > Albert > G2 > M3 > G3 > M4 > G4 >

Step Two: Elaine is two persons removed from Joseph (from Line 2) so either:

#A Peter > G1 > Albert > G2 > Joseph > G3 > M4 > Elaine >
#B Peter > Elaine > Albert > G2 > M3 > G3 > Joseph > G4 >

Step Three: In each case, the unknown male must be Paolo.

#A Peter > G1 > Albert > G2 > Joseph > G3 > Paolo > Elaine >
#B Peter > Elaine > Albert > G2 > Paolo > G3 > Joseph > G4 >

Step Four: Liza is two persons removed from Paolo (from Line 3).

#A Peter > Liza > Albert > G2 > Joseph > G3 > Paolo > Elaine >
#B Peter > Elaine > Albert > G2 > Paolo > G3 > Joseph > Liza >

Step Five: Linda hates Paolo (from Line 4), so:
In #A, she can't be G3 and must be G2.
In #B, she can't be G2 and must be G3.

#A Peter > Liza > Albert > Linda > Joseph > G3 > Paolo > Elaine >
#B Peter > Elaine > Albert > G2 > Paolo > Linda > Joseph > Liza >

Step Six: In each case, the unknown female must be Amy.

#A Peter > Liza > Albert > Linda > Joseph > Amy > Paolo > Elaine >
#B Peter > Elaine > Albert > Amy > Paolo > Linda > Joseph > Liza >

Step Seven: Linda is hated by the man whom Amy loves (from line 4).
Thus, #B does not work so the solution is #A.

Peter > Liza > Albert > Linda > Joseph > Amy > Paolo > Elaine >

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