The Love Loop on the Love Isaland

What was the puzzle?

There are few hints given in the question.

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1. Peter falls in love with a girl who is unfortunately in love with Albert. 

2. Joseph loves a girl who loves the man who loves Elaine. 

3. Liza is loved by the guy who is loved by the girl who is loved by Paolo. 

4. Linda hates Paolo and is hated by the man whom Amy loves.

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STEPS :

STEP 1 :

Let's name all 4 men as M1, M2, M3 and M4 while girls as G1, G2, G3 and G4.

STEP 2 :

Let's start with Peter. He can be at any position M1, M2, M3 or M4. Let's assume that he is at M1. As (1) points M2 must be Albert.

STEP 3 :

As per (2), there are 2 persons in between Joseph and Elaine. That is Joseph can be at M3 or M4 while Elaine can be at G4 or G1 respectively. Exactly, same are possible locations for Paolo and Liza respectively in the loop as (3) suggests.

STEP 4 :

In short, at M3 and M4, we have Joseph and Paolo and G1, G4 are occupied by Liza and Elaine but exact location yet to be known.

STEP 5 :

For The statement (4) to be TRUE, Linda must be hating Paolo. 

 👉 CASE 5.1 : If Paolo is at M3 then Linda can't be at G2 hence must be at G3. With that, Joseph will be at M4, Elaine at G1, Liza at G4 & only location for Amy as G2.

 👉 CASE 5.2 : If Paolo is at M4 then Linda can't be at G3 hence must be at G2. With that, Joseph will be at M3, Elaine at G4, Liza at G1 & only location for Amy as G3.

CASE 5.1 make other part of the statement (4) false i.e. Linda is hated by man (Paolo here) whom Amy loves is false in the case.

Hence, CASE 5.2 is valid and the final loop looks as - 

Finally, turning to the question asked.

Q. Who loves Joseph and whom does Joseph love?

A. Linda loves Joseph and Joseph loves Amy.