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Mystery Master | Analysis of Hello Dolly | Member |
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Mystery Master | Analysis of Hello Dolly | Member |
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This five-star logic puzzle is one of the harder puzzles to solve. This puzzle has everything to do with capacity. It has only 3 noun types, but there are 20 nouns per type! It also has 5 links, over 400 facts, and 1 rule. It needs 1200 marks, but only 3 grids. The introduction gives us the names, genders, and color outfits of the dolls.
The 10 female dolls are: Annabelle, Ashley, Holly, Jessica, Kirsty, Michelle, Paige, Staci, Tanya and Tiffany.
The colors of their outfits are: 5 pink, 2 red, and 1 each of gold, green, and purple. Exclusive female colors are: pink, gold, and purple.
The 10 male dolls are: Benji, Chad, Damon, Darren, Enrique, Jamie, Joshua, Juan, Keenan and Quentin.
The colors of their outfits are: 5 blue, 2 red, and 1 each of green, silver, and yellow. Exclusive male colors are: blue, silver, and yellow.
So the shared colors are: red for 2 females and 2 males, green for 1 female and 1 male. Just specifying what colors the dolls cannot wear takes up the first 200 facts!
The introduction also tells us the dolls are in two cabinets A and B that faces each other. They sit in slots numbered from 1 to 10 from left to right. So A01 faces B01, A02 faces B02, and so on all the way to A10 faces B10. The links that define the relationships between the slots are with, next to, one away from, and across from. For the first 3 links, the dolls must sit in the same cabinet. For the last link they sit in different cabinets, but have the same slot number.
Clue 1 states "No doll wearing pink is next to another doll wearing pink and no doll wearing blue is next to another doll wearing blue." This takes the next 20 facts. If there was a rule, it would need to examine the possible placements of the pinks and blues.
Clue 2 states "Female dolls are at each end of a row, only one of those females has another female next to her." The first part of this clue means that no males are in slots A01, A10, B01, and B10. This takes the next 40 facts. The second part of this clue will need to be enforced by a rule.
The introduction and the first two clues take up the first 260 facts, but are very straight-forward.
To see what dolls are pink, let's examine clue 3 with an eye on clues 6 and 9.
Clue 3 states "The five dolls with pink outfits are (in some order): Tiffany, two females across from each other (one between two males and the other between two females, in some order), the doll next to Keenan and the doll across from the female in green." So there is at least one pink doll in each row.
Clue 6 states "The four dolls in red are: Juan, the male across from Juan, the female next to that male and Paige." So there is at least one red doll in each row.
Clue 9 states "Jessica (who is not next to Staci) and Ashley are at the left and right ends of row B, respectively, and wear the same color outfit."
Because clue 6 states page is wearing red, that leaves pink as the only color both Jessica and Ashley could wear (clue 9). So we have the following unique assignments.
Note that Pink2 and Pink3 is reserved for the doll next to Keenan, and for the doll across from the female in green. So while either Jessica or Ashley is next to Keenan (in either B02 or B09), the other one is across from the female in green (Green1 in either A01 or A10).
Clue 4 states "The dolls with blue outfits are (in some order): two males who are across from each other (each next to a female in a pink outfit who are at the end of a row), Quentin, the doll across from Paige and the doll between Annabelle and Enrique (who is wearing red)." So there is at least one blue doll in each row. So let's break this down.
Since there are no other restrictions on them, I will assign Pink4 and Blue1 to row A, which means Pink5 and Blue2 are in row B.
Clue 5 states "The six males in row A are (in some order): the three males next to each other, two males next to each other (dressed in green and red, in some order and flanked by the female in gold and Holly, in some order), and the only male not to have another male next to him.".
The two males next to each other in row A are dressed in Green2 and Red (Red3 or Red4). They are flanked by females, one in Gold1 and the other is Holly. So Holly is not wearing Gold1. Holly can be in A01, A03 - A08, or A10.
Below are the 6 possible layouts for row A.
1 FMMMFMMFMF or 2 FMFMMFMMMF (reverse of 1) 3 FMMMFMFMMF or 4 FMMFMFMMMF (reverse of 3) 5 FMMFMMMFMF or 6 FMFMMMFMMF (reverse of 5)
This shows that the females in the end slots for row A must be next to a male. So to satisfy clue 2, either slot B02 or B09 must contain a female.
This also shows that two females cannot be next to each other in row A. Since clue 3 has three females next to each other, they must be in row B.
Earlier I assigned Pink4 and Blue1 to row A, and Pink5 and Blue2 to row B. From clue 6, this means Pink4 is between two males, and Pink5 is between two females. So Pink4 must be in slots A03 - A08, and Pink5 must be in slots B03 - B08. Likewise, Blue1 must in slots A02 or A09 and Blue2 in slots B02 or B09.
Clue 6 states "The four dolls in red are: Juan, the male across from Juan, the female next to that male and Paige." Because we want the girls to have the first two reds, let's make the following assignments.
So looking at Red1 and Red3, what the first assignment really means is "The female wearing Red1 is next to the male wearing Red3."
Clue 7 states "The two dolls in green are a male and female next to each other in row A." Green1 is for the female doll across from the female wearing Pink5 (clue 3). Green2 is for the male next to Green1. Since both greens are in row A, Pink5 is in row B.
From clue 5, two males, next to each other dressed in green (Green2) and red (Red3 or Red4), are just between the female in gold (Gold1) and Holly. Since the male in green (Green2) has the male in red on one side, he must have the female in green on the other side. This means the male in green (Green2) is next to Holly, and Holly must be wearing green (Green1).
So next to Holly (Green1) is the male in green (Green2), who is next to the male in red (Red3 or Red4), followed by the female in gold (Gold1).
Clue 6 states "The four dolls in red are: Juan (Red4), the male (Red3) across from Juan, the female (Red1) next to that male (Red3), and Paige (Red2)." Since clue 4 told us that Enrique is wearing red, he is the male wearing Red3. Looking at clue 5 again, the males in green and red are flanked by a female in gold and Holly in green. Therefore the male doll wearing red in row A must be Juan, since Enrique must be next to a female doll wearing red.
Clue 8 states "Darren is dressed in yellow and he is across from the male dressed in silver." There is only one yellow outfit, and only one silver outfit, and they are both for the male dolls, so this clue is straightforward.
Clue 9 states "Jessica (who is not next to Staci) and Ashley are at the left and right ends of row B, respectively, and wear the same color outfit." Therefore, B01 contains Jessica, and B10 contains Ashley. Earlier we assigned Pink2 to Jessica, and Pink3 to Ashley.
Clue 10 states "Jamie is flanked by Kirsty (with Tanya across from her) and Benji, in some order." This means Jamie is next to Kirsty and Jamie is next to Benji, and that Kirsty and Benji are one slot away from each other. And finally, Kirsty is across from Tanya.
Clue 11 states "Michelle and Joshua are across from each other and Chad is not wearing blue."
Row A Slots : A01:Female, A10:Female, A02:Male, A09:Male Dolls : Holly:Green1 across B01:Pink2 or B10:Pink3, Juan:Red4 Colors : females: Pink4 (between 2 males) across Pink5, Gold1, Green1; males: Blue1, Green2, Red4 Genders: 6 males, 4 females Row B Slots : B01:Jessica,Pink2, B10:Ashley,Pink3, Male in either B02 or B09 Dolls : Jessica, Ashley, Enrique:Red3, Keenan in B02 or B09 Colors : females: Pink2, Pink3, Pink5 (between 2 females), Red1, Red3; males: Blue2 Genders: 4 males, 6 females Enrique:Red4 is across from Juan:Red4, and Enrique is next to female in Red1.
If the program solves the puzzle using levels 1 and 2, we have 960/1200 marks and 14/60 pairs. We find Keenan is Blue2. Unfortunately, there are nearly 100 facts left to examine. This means level 3 may be slow.
With level 3, the program is able to solve the puzzle in a very reasonable amount of time! I think what was very helpful was assigning the pink colors.
Recap for "Just Between".There are four instances where the clues specify a noun is just between two other nouns. I was able to satisfy this relationship by using two "next to" links. If the two outside nouns had different noun types, I would also have to state they are not together.
This is a very challenging five-star puzzle that requires a lot of thought. Make sure your IQ is up to it.