wodin

Based on the information given by the beam and truth booth ceremonies to date, there are only four possible solutions to the game: Solution 1: Zak & Kayla, Tevin & Kenya, Kwasi & Bria, Brett & Nutsa, Cam & Morgan, Tomas & Lauren, Shamoy & Maria, Andrew & Samantha, Moe & Jasmine, Daniel & Cali, Lewis & Asia. The next three solutions have the following couples in common: Zak & Morgan, Tevin & Kenya, Kwasi & Asia, Brett & Bria, Tomas & Lauren, Shamoy & Maria, Andrew & Samantha, Moe & Kayla. The remaining possible couple combinations that complete the solutions are: Solution 2: Cam & Jasmine, Daniel & Cali, Lewis & Nutsa. Solution 3: Cam & Nutsa, Daniel & Cali, Lewis & Jasmine. Solution 4: Cam & Nutsa, Daniel & Jasmine, Lewis & Cali. It would seem that, of the four possible solutions given above, Solution 1 is the most probable.

@Racj82 and @snarts;: I have tried to post a comment on your information that the cast is not allowed to use pencils and paper but any time I try to post more than a few sentences it won't work. Very briefly, those items are necessary for one person to work out a solution alone; however, it would be possible to emulate what we at home do with pencil and paper by reproducing each week's beams ceremony using the couples themselves (which we know they are allowed to do) and relying on the collective memory of the cast members to replace our paper memory. If this post works, it will be my last on this very frustrating site.

@PamelaMaeSnap: At the end of week 9 there was enough information to limit the number of possible solutions to seven. The information gained in week10 eliminated six of those solutions and left only one unique solution possible.

@PamelaMaeSnap: As your daughter and friend obviously know, this game requires a straightforward application of deductive logic. All that was required to solve the puzzle was a bit of time and patience, and a minor amount of ingenuity.

@OnceSane - As I posted in S06.E10 there was sufficient information available to the cast at the end of week 10 to enable them to completely solve the 11 perfect matches. I gave the complete solution in that post. The solution included Tyler & Nicole as a perfect match, which was confirmed on last night's show. It also showed that the four perfect matches (other than Tyler & Nicole) in last night's beams ceremony were Kareem & Diandra, Keith & Jada, Michael & Keyana and Clinton & Geles. All of the other couples in that ceremony are no matches, as confirmed by the solution I gave in S06.E10. @Caseysgirl - I believe that all of the "perfect matches" the producers stipulate are plausable matches but they make sure that there are two, three or four plausable matches for each cast member to make it difficult to easily arrive at the 11 "perfect matches". However, that leaves a great many obvious no matches for each cast member and it would be easy to engineer a couples matchup that gives zero beams. That would be an obvious strategy to do in the first beams ceremony and then, having this information, you could test various plausible matches in subsequent beams ceremonies by switching partners between only two couples at a time. The producers understand this and that is why they have introduced an extreme penalty for getting no beams in a beams ceremony.

After the most recent episode S06.E10, we have enough information to solve the game. In my S06.E08 and S06.E09 posts I described how my analysis of the information to the end of week 9 limited the possible solutions to the game to seven , as set out in items (1) to (7) in my last S06.E09 post. In the most recent episode it was confirmed that Michael and Audrey (couple 609) was a no match. As I pointed out in my last S06.E09 post, having couple 609 as a no match further limited the possible solutions to only the three items (5), (6) and (7). The couples in the beams ceremony in the most recent episode are given in item (8) below: (8) 103, 201, 308, 409, 507, 606, 704, 802, 905, 1010, 1111 Comparison of this item (8) with items (5), (6) and (7) shows that, if either item (5) or (6) were the solution there would have been only two beams in the most recent beams ceremony. There were three beams so that eliminates both items (5) and (6). However, item (7) gives three beams and, since it is the only possibility left, it is the solution which gives the correct 11 perfect matches, as follows: 111 - Kareem & Diandra; 204 - Anthony & Alexis; 301 - Malcolm & Alivia; 407 - Keith & Jada; 508 - Joe & Uche; 606 - Michael & Keyana; 705 - Ethan & Zoe; 802 - Clinton & Geles; 909 - Shad & Audrey; 1010 - Tyler & Nicole; 1103- Dimitri & Nurys The beams in weeks 2 through 10 were: 2 - 606, 909 and 1010; 3 - 606; 4 - 1010 and 1103; 5 - 301, 909 and 111; 6 - 909; 7 - 301, 802, 909, and 1010; 8 - none; 9 - 407, 508, 705, 802 and 1010; 10 - 606, 802 and 1010 Please note that, in the list of couples for the beam ceremony in week 4 that I gave in my S06.E08 post, couple 903 should have been 906 and 1106 should have been 1103. The contestants have shown great concern about not getting any confirmed perfect matches but I have shown that it is possible to solve the game based on only the no match and beam ceremony information to date, without any confirmed perfect matches.

Since the posting I just tried worked I will try another. This is a continuation of my post in the discussion of the previous episode S06.E08. There I set out my numbering system for designating the couples and outlined the procedures for testing what combinations of perfect matches and no matches logically comply with all the information revealed to date. Please note that there was one error in setting out the couples that participated in the third couples/beams ceremony in week 4. I had included couples Shad and Nurys (903) and Dimitri and Keyana (1106) when the couples should have been Shad and Keyana (906) and Dimitri and Nurys (1103). I have corrected this for my present and future analyses. The error did not affect the conclusion arrived at in my post in S06.E08. However, the information gained in the most recent episode S06.E09 did affect the previous tentative conclusion which was based solely on the assumption that Kareem and Alivia (101) was a perfect match. This assumption leads to the conclusion that there should have been only four beams in week 9. Since there were actually five beams this means that couple 101 is not a perfect match. Back to the drawing board. The first couples/beams ceremony in week 2 showed beams for the following couples: 101 - Kareem & Alivia, 202 - Anthony & Geles, 303 - Malcolm & Nurys, 404 - Keith & Alexis, 505 - Joe & Zoe, 606 - Michael & Keyana, 707 - Ethan & Jada, 808 - Clinton & Uche, 909 - Shad & Audrey, 1010 - Tyler & Nicole, 1111 - Dimitri & Diandra. Four of the couples in week 2 (couples 202, 303, 404 and 808) have been confirmed as no matches in the truth booth. To this we can add couple 101 as a no match. This leaves six couples (505, 606, 707, 909, 1010, 1111), of which three are perfect matches. There are exactly 20 ways to choose three couples from six couples (without regard to order). I have workrd through all of these 20 possible combinations of three couples. Seventeen combinatoions can be eliminated as leading to a logical inconsistency based on the information to date. The only combinations of three couples from week 2 which do not lead to any logical inconsistencies based on the information to date are: (a) 505 -Joe & Zoe, 707 - Ethan & Zada, 1010 - Tyler & Nicole (b) 505 - Joe & Zoe, 707 - Ethan & Jada, 1111 - Dimitri & Diandra (c) 606 - Michael & Keyana, 909 - Shad & Audrey, 1010 - Tyler & Nicole In the the upcoming episode, either Joe and Alivia (couple 501) or Michael and Audrey (609) will be sent to the truth booth. If Joe and Alivia are sent to the truth booth they will be confirmed as a no match since combinations (a) and (b) above require Joe and Zoe (505) to be a perfect match and, from my analysis, combination (c) requires Joe to be martched with Uche (508). Remember that combinations (a), (b) and (c) are the only possibilities - so Joe and Alivia must be a no match. However, if Michael and Audrey (couple 609) are sent to the truth booth then we have the following: If couple 609 are confirmed as a perfect match then this eliminates combination (c) because it requires 606 as a perfect match and my analysis eliminates combination (a) because it needs 602 or 611 as a perfect match. However, it confirms combination (b) and then there would be only four possible complete 11 perfect matches as follows: (1) 110, 206, 304, 403, 505, 609, 707, 802, 908, 1001, 1111 (2) 108, 206, 304, 403, 505, 609, 707, 802, 910, 1001, 1111 (3) 108, 206, 310, 403, 505, 609, 707, 802, 901, 1004, 1111 (4) 104, 206, 310, 403, 505, 609, 707, 802, 901, 1008, 1111 If couple 609 are a confirmed no match, this eliminates combination (b) which requires 609 to be a perfect match. However, combinations (a) and (c) would still be possible and this leads to only three possible complete 11 perfect matches (items (5) and (6) being under combination (a) and item (7) being under combination (c)): (5) 103, 206, 304, 408, 505, 602, 707, 811, 901, 1010, 1109 (6) 108, 206, 304, 403, 505, 611, 707, 802, 901, 1010, 1109 (7) 111, 204, 301, 407, 508, 606, 705, 802, 909, 1010, 1103 To summarize, if 609 is confirmed as a perfect match then the solution to the game is one of items (1), (2), (3) or (4). If 609 is a no match then the solution is one of items (5), (6) or (7). A decent strategy for the contestants if 609 is not confirmed as a perfect match would be to couple up as in item (7) when the couple to be sent to the truth booth is to be chosen. This is because having any of the couples in item (7) except 802 or 1010 declared as a perfect match would determine item (7) to be the solution to the game. Other strategies are obvious from the seven possible solutions given above, depending on what answer they get from the upcoming truth both.

@caseygirl I have tried to post to this discussion several times in the recent past but have been sucessful only once. When nothing happens after tapping the submit reply button there is no explanation as to why the posting did not happen. Perhaps the reason there are only 5 or so people posting is that others have given up trying. I decided to try once more. Here goes.

I tried to post this on this site early yesterday but it didn't work; here goes another try. For convenience and ease of listing, number the contestants as follows: 1 - Kareem, 2 - Anthony, 3 - Malcolm, 4 - Keith, 5 - Joe, 6 - Michael, 7 - Ethan, 8 - Clinton, 9 - Shad, 10 - Tyler, 11 - Dimitri, 01 - Alivia, 02 - Geles, 03 - Nurys, 04 - Alexis, 05 - Zoe, 06 - Keyana, 07 - Jada, 08 - Uche, 09 - Audrey, 10 - Nicole, 11 - Diandra Each possible male/female couple is designated by a number as follows: 101 = Kareem & Alivia, 602 = Michael & Geles, 1111 = Dimitri & Diandra, and so on. It is easy to list all of the 121 possible couples by listing the numbers 101 to 111 then 201 to 211 then 301 to 311 and so on down to 1001 to 1011 and finally 1101 to 1111. We have the following data: Week 1 - Confirmed no match (CNM) = 706; no couples/beams ceremony. Week 2 - CNM = 202; Beams = 3; Couples = 101, 202, 303, 404, 505, 606, 707, 808, 909, 1010, 1111. Week 3 - CNM = 303; Beams = 1; Couples = 101, 902, 303, 404, 1005, 606, 707, 808, 509, 1110, 211. Week 4 - CNM = none; Beams = 2; Couples = 101, 207, 302, 411, 505, 609, 704, 808, 903, 1010, 1106. Week 5 - CNM = 1110; Beams = 3; Couples = 301, 602, 403, 1104, 505, 206, 1007, 808, 909, 710, 111. Week 6 - CNM = 808; Beams = 1; Couples = 101, 210, 311, 404, 505, 603, 702, 807, 909, 1006, 1108. Week 7 - CNM = 404; Beams = 4; Couples = 301, 802, 103, 504, 405, 206, 707, 608, 909, 1010, 1111. Week 8 - CNM = 401; no couples/beams ceremony. Weeks 3 and 6 had only one beam. The only couples who were in both weeks were 101 and 404. Couple 404 was a confirmed no match in week 7. That leaves couple 101 (Kareem & Alivia) as the only couple in both weeks and, though there is no guarantee, it is a decent assumption to make that they are the one perfect match given in weeks 3 and 6 (despite the blowup in week 8). Based on this assumption, none of the other couples in weeks 3 and 6 would be perfect matches. Indicate 101 as a perfect match on the list of 121 possible couples and strike off all confirmed no matches and the other no match couples from weeks 3 and 6. When this is done, look at week 2. The only couples in week 2 that have not been indicated as no matches (other than 101) are 1010 and 1111. Since there were 3 beams in week this would mean that, given the assumption that 101 is a beam and given the confirmed no matches and the information in weeks 3 and 6, the three perfect matches in week 2 were 101, 1010, and 1111. Whenever we get an indication of a perfect match couple this allows us to eliminate quite a few more couples from the list of 121 couples as no matches. Thus we can eliminate all couples from 102 to 111, all couples from 1001 to 1011 (except 1010 who are a perfect match), and all couples from 1101 to 1110. Furthermore, we can eliminate all couples for whom the last two digits equal the last two digits of the perfectly matched couple(s). In this case we eliminate all couples with the last two digits of 01, 10 or 11 - except, of course our perfect match couples 101, 1010 and 1111. Having done this, we move to week 5. We notice now that the only three couples in week 5 that have not been eliminated as no matches are 602, 403 and 206. Since there were three beams in week 5, these three couples must be the perfect matches in that week. Indicate them as such and follow the procedure outlined in the previous paragraphs for designating no matches based on the information that 602, 403 and 206 are perfect matches and the males and females in those perfect match couples cannot be matched with anyone else. Having done this, move to week 7. In week 7, couples 206, 1010 and 1111 (which we have already indicated as perfect matches) account for three of the four beams. The only other couple in that week that has not been designated as a no match is 504. This must be the fourth perfect match in week 7. Indicate them as such and go through the no match elimination procedure in the list of 121 possible couples that this perfect match allows you to do, as described above. We now move to the last remaining week, week 4. The only two couples there that have not been designated as no matches in the preceding procedure are 101 and 1010 - but we have already designated these two couples as perfect matches, thus accounting for the two beams in week 4. We have now determined that, based on the assumption that couple 101 is a perfect match and on all the other information given in weeks 1 to 8, the following are perfect matches. (Of course, if 101 is not a perfect match, the analysis fails.) Perfect matches: 101 - Kareem & Alivia, 206 - Anthony & Keyana, 403 - Keith & Nurys, 504 - Joe & Alexis, 602 - Michael & Geles, 1010 - Tyler & Nicole, 1111 - Dimitri & Diandra. This leaves Malcolm (3), Ethan (7), Clinton (8), Shad (9), Zoe (05), Jada (07), Uche (08) and Audrey (09) as remaining to be matched. To be consistent with the foregoing information, there are only seven couple combinations possible for this remaining group: a - 805, 307, 709, 908 b - 805, 308, 709, 907 c - 805, 309, 708, 907 d - 809, 305, 708, 907 e - 809, 307, 705, 908 f - 809, 307, 708, 905 g - 809, 308, 705, 907

After week 8 there was enough information for the contestants to determine the "perfect" matches. They are Kam & Edward, Tayler & Ozzy, Kari & Mike, Casandra & Derrick, Carolina & Hayden, Tyranny & Jaylan, Gianna & Andre, Hannah & Osvaldo, Alicia & Michael, Kathyrn & Joey, Shannon & Tyler