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  Logic Puzzles  | 1  DEL FINADO, Pebielyn B. 1:30  –  3: 00 TTh P505 Saint Louis University Department of Mathematics A Final Project in GMATH: Compilation of Researched Problems with Solution in Mathematics in the Modern World Topic: Logic Puzzles No. of Assigned Problems: 15 No. of Problems Submitted: 15 Name: DEL FINADO, Pebielyn B. Schedule: 1:30  –   3:00 TTH P505 Date Due: April 30, 2019 Date Submitted: April 30, 2019    Logic Puzzles  | 2  DEL FINADO, Pebielyn B. 1:30  –  3: 00 TTh P505 1.   Whose Fish? (logic puzzle) First, set up a 6×5 matrix of attributes then started highlighting and crossing out relevant details. Intuitively, I knew it all came down the Norwegian. This because we know he has only one neighbor. Everyone else can have one or two neighbors. Eventually, it came down to coffee (consumed and in clue 5). The Puzzle: There are five houses in a row in different colors. In each house lives a person with a different nationality. The five owners drink a different drink, smoke a different brand of cigar and keep a different pet, one of which is a Walleye Pike. Who owns the fish? The 15 clues: 1.   The Brit lives in the red house. 2.   The Swede keeps dogs as pets. 3.   The Dane drinks tea. 4.   The green house is on the left of the white house. 5.   The green house owner drinks coffee. 6.   The person who smokes Pall Malls keeps birds. 7.   The owner of the yellow house smokes Dunhills. 8.   The man living in the house right in the center drinks milk. 9.   The man who smokes Blends lives next to the one who keeps cats. 10.   The Norwegian lives in the first house. 11.   The man who keeps horses lives next to the one who smokes Dunhills. 12.   The owner who smokes Bluemasters drinks beer. 13.   The German smokes Princes. 14.   The Norwegian lives next to the blue house. 15.   The man who smokes Blends has a neighbor who drinks water. The end of this puzzle will have five units, each with 6 attributes: {address, house color, nationality, drink, pet and smokes} The data seems to break down into two types: Definitive data, that which defines an attribute directly within one unit. And relational data, which defines an attribute relative to another unit. Relational data often acts as a negating definition as well, showing what isn’t in a unit by describing what’s nearby.   Now stepping through the clues, definitive data related to nationality first: 1. The Brit lives in the red house.  Brit == red 2. The Swede keeps dogs as pets. Swede == dogs 3. The Dane drinks tea.  Dane == tea 10. The Norwegian lives in the first house.  Norwegian == 1st house  Logic Puzzles  | 3  DEL FINADO, Pebielyn B. 1:30  –  3: 00 TTh P505 13. The German smokes Princes. German == Princes  Next comes the secondary definitions. These can be used to reveal data which eliminates  possible units based on what is already known: 5. The green house owner drinks coffee. Coffee == Green ∴   Brit != coffee  Dane != Green 6. The person who smokes Pall Malls keeps birds.  Pall Malls == birds ∴  German != birds Swede != Pall Malls 7. The owner of the yellow house smokes Dunhills. Yellow == Dunhills ∴  German != Yellow  Brit != dunhills 8. The man living in the house right in the center drinks milk.  Milk == 3rd House ∴   Norwegian != milk  Dane != 3rd House 12. The owner who smokes Bluemasters drinks beer.  Bluemasters = beer ∴  German != beer  Dane != Bluemasters First Second Third Fourth Fifth Blue Green Red White Yellow Brit Dane German Norwegian Swede Beer Coffee Milk Tea Water Birds Cats Dogs Fish Horses Blends Bluemasters Dunhills Pall Malls Princes First Second Third Fourth Fifth Blue Green Red White Yellow Brit Dane German Norwegian Swede Beer Coffee Milk Tea Water Birds Cats Dogs Fish Horses Blends Bluemasters Dunhills Pall Malls Princes First Second Third Fourth Fifth Blue Green Red White Yellow Brit Dane German Norwegian Swede Beer Coffee Milk Tea Water  Logic Puzzles  | 4  DEL FINADO, Pebielyn B. 1:30  –  3: 00 TTh P505 Birds Cats Dogs Fish Horses Blends Bluemasters Dunhills Pall Malls Princes First Second Third Fourth Fifth Blue Green Red White Yellow Brit Dane German Norwegian Swede Beer Coffee Milk Tea Water Birds Cats Dogs Fish Horses Blends Bluemasters Dunhills Pall Malls Princes First Second Third Fourth Fifth Blue Green Red White Yellow Brit Dane German Norwegian Swede Beer Coffee Milk Tea Water Birds Cats Dogs Fish Horses Blends Bluemasters Dunhills Pall Malls Princes   Many of the relational data clues reveal additional information about what a unit doesn’t have:   4. The green house is on the left of the white house. Green = White’s address –   1 9. The man who smokes Blends lives next to the one who keeps cats.  Blends = Cat’s address ± 1 ∴   Blends != cats 11. The man who keeps horses lives next to the one who smokes Dunhills.  Horses = Dunhills’ address ± 1 ∴   Dunhills != horses  Horses != Yellow 14. The Norwegian lives next to the blue house.  Blue = 2nd house ∴   Brit != 2nd house  Norwegian != Blue 15. The man who smokes Blends has a neighbor who drinks water.  Blends = Water’s address ± 1 ∴   Blends != water The fourteenth clue is one of the most important. Since we know the Norwegian lives in the 1st house (clue 10), we know that the blue house is number 2. Number 4 is a tricky one, there is no reason to believe that the green house is the first house, all we know is that the white house is on it’s left. Also, clues 9 and 15 could be referring to one or two neighbors.   It’s interesting that the clues sort out into three quintuplets.   Here’s where it starts to get really hard. All that is known for certain is what was defined i n questions 1- 3, 10 and 13. There remain three or four unknowns for each unit. What I’m looking for is the first link in a causality chain. Of course it’s probably not so much a chain as a loop, so looking for an end is futile. How about an onramp? After several minutes of staring, and re-reading the clues, I got the chills (really!)
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