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Dinner Party Riddle

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Helen and her husband invited their neighbors (four members) for a dinner at home. The six of them sat at a round table. Helen tells you the following:

“Victor sat on the left of the woman who sat on the left of the man who sat on the left of Anna.
Esther sat on the left of the man who sat on the left of the woman who sat on the left of the man who sat on the left of the woman who sat on the left of my husband.
Jim sat on the left of the woman who sat on the left of Roger.
I did not sit beside my husband.”

What is the name of Helen’s husband?

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SherlockHolmes Expert Asked on 26th January 2018 in Logic Puzzles.
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    • 2 Answer(s)

    ROGER

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    krishnaprasath Starter Answered on 26th January 2018.

    SherlockHolmes

    How?

    on 27th January 2018.
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    Viji_Pinarayi

    See detailed explanation in my answer below.

    on 30th January 2018.
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    From the statements, it is evident that the hosts and the guests were seated in an alternating Male – Female arrangement.
    Thus, we have the general arrangement as in Fig. 1. (‘M’ and ‘F’ indicate Male and Female participants of the party. Seats are numbered for ease of reference.)

    Since the first statement regarding the seating arrangement talks about the position of Victor, let us start by placing him in one of the ‘M’ seats, say, Seat No. 1. (Can be 3 or 5 as well, makes no difference except for corresponding change in the seat taken by Anna) Then we have the seat positions as in Fig. 2.

    Statement 2 mentions the placement of Esther. There are only two ‘F’ seats (2 and 6) that could be occupied by her. If we assume that she was seated at No. 2, the second statement would mean that she sat on the left of the man (Victor) who sat on the left of the woman (S6) who sat on the left of the man (S5) who sat on the left of the woman (S4) who sat on the left of Helen’s husband. This would mean that the man who occupied S3 must be Helen’s husband.

    Statement 3 describes Jim’ placement. He could be either at S3 or S5, the only remaining ‘M’ seats. However, he can’t be at S3 because, as per statement 3, he sat on the left of the woman (S2) who sat on the left of Roger, which would contradict our original placement as per which seat 1 is taken by Victor. Hence, Jim must be at S5, which, in turn, means that S3, the only remaining ‘M’ seat, must be occupied by Roger. Thus, as per the deduction from statement 2 above, Helen’s husband must be ROGER. Thus, we get the seat placement as in Fig. 3.

    Now, the only remaining seat is S6 which must be occupied by Helen. (This also satisfies the last statement that Helen did NOT sit beside her husband. This completes the seating arrangement.
    ————————————————————————————————————————–

    In the above sequence, we had assumed that Esther was seated at S2. Now, if we take the other possible scenario in which she was seated at S6, the ‘left of left of…’ sequence in the statement 2 would mean that Victor was Helen’s husband, because Esther sat “on the left of the man (S5) who sat on the left of the woman (S4) who sat on the left of the man (S3) who sat on the left of the woman (S2) who sat on the left of” Helen’s husband. This leaves Helen seated at S2, the only ‘F’ seat remaining. However, this contradicts the final statement according to which Helen did NOT sit beside her husband whereas S2 is beside Victor who, as per the assumption, is her husband.

    Thus, we can conclude that this alternate assumption is NOT possible.

    Hence, the result: Helen’s husband is ROGER, and we have the final seat arrangement as per fig. 4.

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    Viji_Pinarayi Expert Answered on 28th January 2018.
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