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Logic Problem
Whose Fish?
By Albert Einstein (maybe)

This brainteaser, reportedly written by Einstein is difficult and Einstein said that 98% of the people in the world could not figure it out. Which percentage are you in?

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.

The question is-- who owns the fish?

Hints:
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.

logic.rb

 1	 #!/usr/bin/env ruby
 2	 ############################
 3	 # SOLUTION by Joby Bednar:
 4	 #
 5	 # Logic Puzzle Solver - brute force with staggered calculation and testing.
 6	 # Applies calculations and tests logic in layers: merging one layer at a time
 7	 # using logic tests for those layers involved.  Reduces number of tests from
 8	 # 373,248,000,000 ( 5!^5 * 15, from brute forcing all combinations with all 15 tests ) 
 9	 # to a managable 50,000!
 10	 # ( less if final test is stopped when 1st solution is found)
 11	 #
 12	 # This is by no means the most efficient order of combinations and tests.
 13	 # It would be interesting to devise a way to determine what the most
 14	 # effective order would be given this method of solution.
 15	 #
 16	 ############################
 17	 # Possibility Class used for Combination calculation
 18	 #    http://jobybednar.com/dev_permutation.asp
 19	 #
 20	 class Possibility
 21	         attr_reader :count, :table, :type, :params, :c_size
 22	 
 23	         def initialize(params=Array.new)
 24	                 @count = 0
 25	                 @table = Array.new
 26	                 @type = ""
 27	                 @params = params
 28	         end
 29	 
 30	         def getCombos(size=@params.length)
 31	                 @c_size = size
 32	                 @type = "combination"
 33	                 @table.clear
 34	                 combination(@params,Array.new)
 35	                 @table.uniq!
 36	                 @count = @table.length
 37	                 return @count
 38	         end
 39	 
 40	    private
 41	 
 42	         #recursive function for combinations
 43	         def combination(params,str)
 44	                 if(str.length == @c_size)
 45	                         @table.push(str)
 46	                 else
 47	                         if(params.length == 1)
 48	                                 @table.push(str.push(params[0]))
 49	                         else
 50	                                 params.each_with_index do |item,i|
 51	                                         newstr = str.dup.push(item)
 52	                                         newparams = params.dup
 53	                                         newparams.slice!(i)
 54	                                         combination(newparams,newstr)
 55	                                 end
 56	                         end
 57	                 end
 58	                 return 0
 59	         end
 60	       
 61	 end
 62	 
 63	 ########################################
 64	 # Program Start
 65	 
 66	 t = Time.now
 67	 tests = 0 #counter
 68	 
 69	 #test 10
 70	 puts "--WHO--\ntest 10"
 71	 who = []
 72	 #Brit, Swede, Dane, Norwegian, German
 73	 w = Possibility.new( ["BR","SW","DA","NO","GE"] ) 
 74	 w.getCombos(5)
 75	 w.table.each do |combo|
 76	    #test 10
 77	    tests+=1
 78	    if combo[0] == "NO" 
 79	       who << combo
 80	    end
 81	 end
 82	 puts "size: #{w.count} >> #{who.size}"
 83	 
 84	 #test 4
 85	 puts "--COLOR--\ntest 4"
 86	 color = []
 87	 #Red, White, Green, Yellow, Blue
 88	 c = Possibility.new( ["RD","WT","GR","YL","BL"] ) 
 89	 c.getCombos(5)
 90	 c.table.each do |combo|
 91	    #test 4
 92	    tests+=1
 93	    if combo[0] != "WT" and combo[combo.index("WT")-1] == "GR"
 94	          color << combo
 95	    end
 96	 end
 97	 puts "size: #{c.count} >> #{color.size}"
 98	 
 99	 #test 8
 100	 puts "--DRINKS--\ntest 8"
 101	 drinks = []
 102	 #Tea, Coffee, Milk, Beer, Water
 103	 d = Possibility.new( ["TE","CF","MK","BE","WA"] ) 
 104	 d.getCombos(5)
 105	 d.table.each do |combo|
 106	    #test 8
 107	    tests+=1
 108	    if combo[2] == "MK"
 109	       drinks << combo
 110	    end
 111	 end
 112	 puts "size: #{d.count} >> #{drinks.size}"
 113	 
 114	 #puts "--ANIMALS--"
 115	 #Dog, Bird, Cat, Horse, Fish
 116	 a = Possibility.new( ["DG","BD","CT","HR","FH"] ) 
 117	 a.getCombos(5)
 118	 
 119	 #puts "--SMOKES--"
 120	 #Pall Malls, Dunhills, Blends, Blue Masters, Princes
 121	 s = Possibility.new( ["PM","DH","BL","BM","PR"] ) 
 122	 s.getCombos(5)
 123	 
 124	 #tests 6,9,11
 125	 puts "--ANIMAL-SMOKES--\ntests 6,9,11"
 126	 an_sm = []
 127	 a.table.each do |comboa|
 128	    s.table.each do |combos|
 129	       tests+=1
 130	       if comboa[combos.index("PM")] == "BD" #test 6
 131	          x = combos.index("BL")
 132	          y = comboa.index("CT")
 133	          tests+=1
 134	          if (x-y).abs == 1 #test 9
 135	             x = combos.index("DH")
 136	             y = comboa.index("HR")
 137	             tests+=1
 138	             if (x-y).abs == 1 #test 11
 139	                an_sm << [comboa,combos]
 140	             end
 141	          end
 142	       end
 143	    end
 144	 end
 145	 puts "size: #{a.count}*#{s.count} >> #{an_sm.size}"
 146	 
 147	 #tests 12,15
 148	 puts "--ANIMAL-SMOKES-DRINKS--\ntests 12,15"
 149	 an_sm_dr = []
 150	 an_sm.each do |combo|
 151	    drinks.each do |drink|
 152	       tests+=1
 153	       if drink[combo[1].index("BM")] == "BE" #test 12
 154	          x = combo[1].index("BL")
 155	          y = drink.index("WA")
 156	          tests+=1
 157	          if (x-y).abs == 1 #test 15
 158	             an_sm_dr << (combo.dup << drink)
 159	          end
 160	       end
 161	    end
 162	 end
 163	 puts "size: #{an_sm.size}*#{drinks.size} >> #{an_sm_dr.size}"
 164	 
 165	 #tests 5,7
 166	 puts "--ANIMAL-SMOKES-DRINKS-COLOR--\ntests 5,7"
 167	 an_sm_dr_cl = []
 168	 an_sm_dr.each do |combo|
 169	    color.each do |hue|
 170	       tests+=1
 171	       if combo[2][hue.index("GR")] == "CF" #test 5
 172	          tests+=1
 173	          if combo[1][hue.index("YL")] == "DH" #test 7
 174	             an_sm_dr_cl << (combo.dup << hue)
 175	          end
 176	       end
 177	    end
 178	 end
 179	 puts "size: #{an_sm_dr.size}*#{color.size} >> #{an_sm_dr_cl.size}"
 180	 
 181	 #tests 1,2,3,13,14
 182	 puts "--ANIMAL-SMOKES-DRINKS-COLOR-WHO--\ntests 1,2,3,13,14"
 183	 answer = []
 184	 found = false
 185	 an_sm_dr_cl.each do |combo|
 186	    who.each do |person|
 187	       tests+=1
 188	       if combo[3][person.index("BR")] == "RD" #test 1
 189	          tests+=1
 190	          if combo[0][person.index("SW")] == "DG" #test 2
 191	             tests+=1
 192	             if combo[2][person.index("DA")] == "TE" #test 3
 193	                tests+=1
 194	                if combo[1][person.index("GE")] == "PR" #test 13
 195	                   x = person.index("NO")
 196	                   y = combo[3].index("BL")
 197	                   tests+=1
 198	                   if (x-y).abs == 1 #test 14
 199	                      answer << (combo.dup << person)
 200	                      #found = true
 201	                   end
 202	                end
 203	             end
 204	          end
 205	       end
 206	       #if found then break end
 207	    end
 208	    #if found then break end
 209	 end
 210	 puts "size: #{an_sm_dr_cl.size}*#{who.size} >> #{answer.size}"
 211	 
 212	 #OUTPUT ANSWER
 213	 print "\nLogic Tests Used: #{tests}\nSolution(s): #{answer.size}\n\n"
 214	 puts "num\tclr\twho\tdrnk\tsmk\tpet"
 215	 puts "---\t---\t---\t----\t---\t---"
 216	 answer.each do |ans|
 217	    0.upto(4) do |i|
 218	       print "#{i+1}:\t#{ans[3][i]}"
 219	       print "\t#{ans[4][i]}"
 220	       print "\t#{ans[2][i]}"
 221	       print "\t#{ans[1][i]}"
 222	       print "\t#{ans[0][i]}\n"
 223	    end
 224	 puts
 225	 end
 226	 
 227	 print "Elapsed Time: #{Time.now-t} secs\n\n"
Output 
--WHO--
test 10
size: 120 >> 24
--COLOR--
test 4
size: 120 >> 24
--DRINKS--
test 8
size: 120 >> 24
--ANIMAL-SMOKES--
tests 6,9,11
size: 120*120 >> 288
--ANIMAL-SMOKES-DRINKS--
tests 12,15
size: 288*24 >> 456
--ANIMAL-SMOKES-DRINKS-COLOR--
tests 5,7
size: 456*24 >> 384
--ANIMAL-SMOKES-DRINKS-COLOR-WHO--
tests 1,2,3,13,14
size: 384*24 >> 1

Logic Tests Used: 51156
Solution(s): 1

num	clr	who	drnk	smk	pet
---	---	---	----	---	---
1:	YL	NO	WA	DH	CT
2:	BL	DA	TE	BL	HR
3:	RD	BR	MK	PM	BD
4:	GR	GE	CF	PR	FH
5:	WT	SW	BE	BM	DG

Elapsed Time: 0.25 secs
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