6.9 Side by Side by Side
by Mark Halpin and Dave Shukan
ANSWER: TONYS
Splitting the provided information into separate clues:
- Within any given house, the house color, jewelry item color, and lawn decoration color are all different.
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- Looking in one direction from her front yard, the limousine rider can see (at least) the motorcycle rider's house and the more distant unicycle rider's house, and thinks the blue color of one of them is very pretty.
- The rider of the penny-farthing lives next to the house with the blue gazing globe on its lawn.
- The Farmer's Almanac reader and the comic book reader are not next-door neighbors.
- The monkey (which does not live in the house with the white picket fence decorating its lawn) lives next to the Jazzercise fan (who has yellow roses decorating her lawn).
- The encyclopedia reader drinks iced tea.
- The yoga fan spends hundreds of dollars a month on new outfits.
- The orange house (which has the band saw) is not next to the yellow house (which has the lathe).
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- When the Pilates fan leaves for her weekly 6:00am session, she always rides past both the white house and the house with the pink flamingos (in some order), rather than risk making engine noise in front of the house with the tiger, whose sleeping habits she does not know.
- The reader of the religious tome does not live next to the house with orange pumpkins decorating the lawn.
- The woman who eats coq au vin does not live next door to either the woman who eats chocolate soufflés or the woman who eats graham crackers.
- Both the pink bracelet wearer and the pizza eater next door sleep uninterruptedly every day from midnight until noon.
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- The woman who drinks espresso wears an orange brooch.
- The swimming fan, who does not ride a unicycle, has seen the tiger next door swallow its owner's blue necklace.
- The pink house (which has the crowbar) is not next to the blue house (which has the wrench).
- The pets of both the encyclopedia reader and the penny-farthing rider run into their respective owners' bedrooms and wake them up in the early hours of most mornings.
- Neither the rider of the hot-air balloon (who does not eat pizza) nor the kickboxing fan next door wears the yellow earrings.
- The graham cracker eater drinks Perrier while wondering why the woman who drinks milkshakes never seems to gain weight.
- The drill press was purchased last month.
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- The pink house and the house with the woman who wears a white tiara are not next to each other or to the house with the iced tea drinker.
- The woman who wears a blue necklace drinks cocktails.
- The comic book reader smiles when her potbellied pig reads over her shoulder.
- The pot roast eater feeds table scraps to her guide dog.
- The romance novel reader, who does not own the goldfish, lives in house #4.
Without loss of generality, the houses can be labelled A-E with the desired numbering (either left-to-right or right-to-left) determined at the end.
From [3a], PILATES cannot be A or E as it requires at least two houses on one side and one house on the other side. If PILATES is B (or D) then [3a] would place TIGER into A (or E) which then leads to a contradiction as [4b] would imply SWIMMING is B (or D). Therefore PILATES is C and the vehicle is either LIMOUSINE or MOTORCYCLE as these are the only two vehicles with engines.
A B C D E
COLOR - - - - -
VEHICLE - - LIMO or MOTORC - -
PET - - - - -
DRINK - - - - -
JEWELRY - - - - -
FOOD - - - - -
ACTIVITY - - PILATES - -
BOOK - - - - -
LAWN - - - - -
TOOL - - - - -
Other 6AM rise
Let us assume from now on (without loss of generality as our partial solution is symmetric) that the driving direction indicated in [3a] is towards A (or equivalently, that the WHITE house and PINK FLAMINGOES are in A or B respectively and the TIGER is in D or E).
If C is LIMOUSINE then:
- If the looking direction indicated in [2a] is also towards A, then one of A and B is BLUE and the other is WHITE. From [5a] the PINK house must be A, C or E, but A is already accounted for and the other two possibilities each result in the ORANGE and YELLOW houses being side-by-side, contradicting [2g].
- If the looking direction indicated in [2a] is towards E, then it places the MOTORCYCLE in D and the UNICYCLE in E. By [4b], SWIMMING cannot be in E (because of UNICYCLE) but since it must be a neighbour to TIGER this means TIGER is E and SWIMMING is D. [4b] then places BLUE NECKLACE in E, [5b] places COCKTAILS in E, [2a] + [1] means that BLUE is D. This then leads to a contradiction as [5a] requires one of PINK, WHITE TIARA or ICED TEA to be in E (PINK can't be next to BLUE due to [4c] and each of the other two items of E are already filled.)
Therefore C is not LIMOUSINE meaning C is MOTORCYCLE.
A B C D E
COLOR WHITE ---------> - - -
VEHICLE - - MOTORCYCLE - -
PET - - - TIGER --------->
DRINK - - - - -
JEWELRY - - - - -
FOOD - - - - -
ACTIVITY - - PILATES - -
BOOK - - - - -
LAWN <------------- PINK FLAMINGOS - - -
TOOL - - - - -
Other 6AM rise
Since one of A and B is WHITE and the other is PINK FLAMINGOS neither of them can be PINK. Neither of them can be BLUE either because [5a] would then force PINK into C or E and either case would leave ORANGE and YELLOW as neighbors which contradicts [2g]. This means that in order to fulfil [4c], PINK and BLUE must be in C and E in some order.
In the opposite direction, TIGER is in D or E. Whichever it is, [4b] implies that BLUE NECKLACE is in the same house and the neighboring SWIMMER'S house is NOT UNICYCLE. Each of these option prevents E from being BLUE (the later by virtue of [2a]), therefore E is PINK and C is BLUE.
A B C D E
COLOR WHITE ---------> BLUE - PINK
VEHICLE - - MOTORCYCLE - -
PET - - - TIGER --------->
DRINK - - - COCKTAIL ------->
JEWELRY - - - BLUE NECKLACE -->
FOOD - - - - -
ACTIVITY - - PILATES <------------ SWIMMING
BOOK - - - - -
LAWN <------------ PINK FLAMINGOS - - -
TOOL - - - - -
Other 6AM rise
From [5a], A and C must be the WHITE TIARA and ICED TEA in some order.
If A is ICED TEA and C is WHITE TIARA then [2e] implies A is ENCYCLOPEDIA. [4d] states that A gets woken early and [3d] states that there are two neighbors that are uninterrupted sleepers; these can therefore only be D & E and therefore, the only remaining place for the PENNY FARTHING mentioned in [4d] is in B. These placements then lead to the following:
- Since C is already BLUE, [2b] implies BLUE GLOBE is A meaning PINK FLAMINGOS is B.
- Since E is already PINK, [3d] implies PINK BRACELET is D and PIZZA is E.
- [4b] states that TIGER (which must be D or E) = BLUE NECKLACE and these can only go in E.
- [4a] states ESPRESSO = ORANGE BROOCH and these can only go in B (all other houses have either a drink or jewelry item placed.)
- The remaining jewelry item must be YELLOW EARRINGS in A.
- Neither BALLOON nor KICKBOXING can be in C (already taken), nor can either be in A (due to [4e]), and since they are neighbors by [4e], they must be in D and E (with the BALLOON in D since PIZZA is in E).
- From [4e] KICKBOXING neighbors BALLOON and from [4b] SWIMMING neighbors TIGER and these two health activities must fill D and E in some order.
The above sequence would mean there is no place left for the JAZZERCISE fan who has YELLOW ROSES from [2d] as no house has both an unallocated health activity and lawn decoration. This contradiction means that A is WHITE TIARA (forcing the positions of WHITE and PINK FLAMINGOS from [1]) and C is ICED TEA (with ENCYCLOPEDIA following from [2e]).
A B C D E
COLOR - WHITE BLUE - PINK
VEHICLE - - MOTORCYCLE - -
PET - - - TIGER --------->
DRINK - - ICED TEA COCKTAIL ------->
JEWELRY WHITE TIARA - - BLUE NECKLACE -->
FOOD - - - - -
ACTIVITY - - PILATES <------------ SWIMMING
BOOK - - ENCYCLOPEDIA - -
LAWN PINK FLAMINGOS - - - -
TOOL - - - - -
Other 6AM rise
Woken early
Consider the location of the PENNY FARTHING. It cannot be B since [2b] requires its neighbor to be the BLUE GLOBE (A already has a lawn decoration and C is BLUE which would contradict [1]). Assume that PENNY FARTHING is in A and the BLUE GLOBE is in B. Following similar reasoning to that above:
- [4d] states that A gets woken early and [3d] states that there are two neighbors that are uninterrupted sleepers; these can therefore only be D & E
- Since E is already PINK, [3d] implies PINK BRACELET is D and PIZZA is E.
- [4b] states that TIGER (which must be D or E) = BLUE NECKLACE and these can only go in E.
- [4a] states ESPRESSO = ORANGE BROOCH and these can only go in B (all other houses have either a drink or jewelry item placed.)
- The remaining jewelry item must be YELLOW EARRINGS in C.
- [4e] implies two possibilities for the BALLOON and KICKBOXING neighbors:
- BALLOON in D and KICKBOXING in E once again leads to no placement for the JAZZERCISE fan who has YELLOW ROSES from [2d]
- BALLOON in B and KICKBOXING in A leads to LIMOUSINE and UNICYCLE on the same side of MOTORCYCLE, contradicting [2a].
Therefore PENNY FARTHING is in D or E. From [2b], it is neighbors with the BLUE GLOBE (which cannot correspond with the BLUE NECKLACE) and from [4d] its owner is woken up early. Since [3d] requires neighboring uninterrupted sleepers these must correspond to A & B and [1] implies PINK BRACELET is B and PIZZA is A.
A B C D E
COLOR - WHITE BLUE - PINK
VEHICLE - - MOTORCYCLE PENNY FARTHING ->
PET - - - TIGER ---------->
DRINK - - ICED TEA COCKTAIL ------->
JEWELRY WHITE TIARA PINK BRACELET - BLUE NECKLACE -->
FOOD PIZZA - - - -
ACTIVITY - - PILATES <------------ SWIMMING
BOOK - - ENCYCLOPEDIA - -
LAWN PINK FLAMINGOS - - <------------ BLUE GLOBE
TOOL - - - - -
Other Uninterrupted Uninterrupted 6AM rise Woken early ---->
Woken early
These placements then lead to the following:
- Only one placement remains for the ESPRESSO and ORANGE BROOCH combination from [4a] and that is D or E (whichever is not occupied by the COCKTAIL and BLUE NECKLACE combination).
- The remaining jewelry item must be YELLOW EARRINGS in C.
- Only one placement remains for the GRAHAM CRACKER and PERRIER combination from [4f] and that is B, with the remaining drink being MILKSHAKE in A.
- With only C, D and E remaining [3c] implies that COQ AU VIN is in E and SOUFFLÉS is in C leaving POT ROAST in D.
- [5d] implies GUIDE DOG is in D, not TIGER, which forces the placements of all the above deduced possibilities for D & E.
- Since D cannot be ORANGE from [1], it must be YELLOW and A is ORANGE.
- Only two placements remain for the JAZZERCISE and YELLOW ROSES combination from [2d] but it can't be E since that would neighbor the GUIDE DOG, not the MONKEY, therefore it must be B.
- From [2a] the UNICYCLE and the LIMOUSINE must be on opposites sides of C and from [4b], D is not the UNICYCLE therefore it must be the LIMOUSINE.
- From [4e], the BALLOON cannot be in A, meaning it is in B (with the remaining vehicle being the UNICYCLE in A) and the neighboring KICKBOXING fan must be in A.
- The remaining health activity is YOGA in E.
A B C D E
COLOR ORANGE WHITE BLUE YELLOW PINK
VEHICLE UNICYCLE BALLOON MOTORCYCLE LIMOUSINE PENNY FARTHING
PET - - - GUIDE DOG TIGER
DRINK MILKSHAKE PERRIER ICED TEA ESPRESSO COCKTAIL
JEWELRY WHITE TIARA PINK BRACELET YELLOW EARRINGS ORANGE BROOCH BLUE NECKLACE
FOOD PIZZA GRAHAM CRACKERS SOUFFLES POT ROAST COQ AU VIN
ACTIVITY KICKBOXING JAZZERCISE PILATES SWIMMING YOGA
BOOK - - ENCYCLOPEDIA - -
LAWN PINK FLAMINGOS YELLOW ROSES - BLUE GLOBE -
TOOL - - - - -
Other Uninterrupted Uninterrupted 6AM rise Woken early
Woken early
Continuing:
- From [4d], C cannot be GOLDFISH (as it cannot "run into the bedroom") nor from [5c] can it be PIG (since the C already has the ENCYCLOPEDIA), therefore it must be MONKEY.
- From [2d], the WHITE PICKETS cannot be C, meaning they must be E (with the remaining lawn decoration being ORANGE PUMPKINS in C).
- Only two placements remain for the COMIC BOOK and PIG combination from [5c]; namely A or B.
- From [3b], the RELIGIOUS TOME cannot be in B or D (or C which already has the ENCYCLOPEDIA). If it were in E, the ALMANAC would need to go in D to avoid neighboring the COMIC BOOK and contradicting [2c] but this leaves GOLDFISH and ROMANCE in the same house, contradicting [6]. Therefore the RELIGIOUS TOME is in A.
- Only one placement now remains for the COMIC BOOK and PIG combination from [5c]; namely in B.
- The remaining pet is the GOLDFISH in A.
- From [6], the ROMANCE NOVEL cannot be in house E (as this can only be House 1 or House 5) and so must be in D with numbering going left-to-right.
- The remaining book is ALMANAC in House 5.
- [2g] and [4c] uniquely determine the tools for each house and the remaining tool is DRILL PRESS in the WHITE house.
HOUSE 1 HOUSE 2 HOUSE 3 HOUSE 4 HOUSE 5
COLOR ORANGE WHITE BLUE YELLOW PINK
VEHICLE UNICYCLE BALLOON MOTORCYCLE LIMOUSINE PENNY FARTHING
PET GOLDFISH PIG MONKEY GUIDE DOG TIGER
DRINK MILKSHAKE PERRIER ICED TEA ESPRESSO COCKTAIL
JEWELRY WHITE TIARA PINK BRACELET YELLOW EARRINGS ORANGE BROOCH BLUE NECKLACE
FOOD PIZZA GRAHAM CRACKERS SOUFFLES POT ROAST COQ AU VIN
ACTIVITY KICKBOXING JAZZERCISE PILATES SWIMMING YOGA
BOOK RELIGIOUS TOME COMIC BOOK ENCYCLOPEDIA ROMANCE NOVEL FARMER'S ALMANAC
LAWN PINK FLAMINGOS YELLOW ROSES ORANGE PUMPKINS BLUE GLOBE WHITE PICKETS
TOOL BAND SAW DRILL PRESS WRENCH LATHE CROWBAR
Other Uninterrupted Uninterrupted 6AM rise Woken early
Woken early