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A Halloween Logic Problem
Colorfully-costumed couples greet and treat children on Elm St.
October 28, 2002
From the introduction, the five Trick or Treat couples live at, consecutively, 101, 103, 105, 107, and 109 Elm St.; each man and woman is planning to wear a different costume, and each couple is giving away a different brand of candy to the neighborhood children. By clue 3, the couple who bought the Snickers bars live next door to (between) John and his wife and the woman masquerading as Cinderella and her husband; so the Snickers pair live in one of the three center homes. Similarly, by clue 8, the couple who are treating the children to Twizzlers live next door to (between) Alice and her husband and to Mr. & Mrs. Voorhees; so the Twizzlers treaters live in a second one of the inside three homes. So, either the couples giving the Snickers and the Twizzlers live next door to each other or they live in 103 and 107 Elm St. (or vice versa). If they live next door to each other, since Alice and her husband don't plan to give out Snickers bars (clue 1), by clue 8, Mr. & Mrs. Voorhees would be giving out the Snickers, and Alice and her husband would live on the other side of the couple treating the kids to Twizzlers. By clue 3, then, John and his wife would be the couple giving away the Twizzlers on Halloween, with the wife going as Cinderella then living in the house on the opposite side of the Snickers couple from John and his wife; or, the wife going as Cinderella and her husband would be giving out the Twizzlers and John and his wife would live on the opposite side of the Snickers couple from them. Trying the first case, by clue 6, the couple whose wife is going as Cinderella don't live at 101 or 109 Elm St.; so they would live in the house inside the fifth couple, with Alice then in the other of the end homes. By clue 12, the third inside house would be that of the couple giving away Whoppers on Halloween, who would be the woman going as Cinderella and her husband. The Lechters would have the end unit, and Mr. Voorhees would be dressing as the Tin Man from The Wizard of Oz. By clue 4, the couple treating the trick or treaters to M & M's live next door to Mr. & Mrs. Myers. If Alice and her husband were giving away the M & M's, John would be Myers--no (19). So, the Lechters would be giving out the M & M's, and the Myerses would be giving out the Whoppers, with Alice and her husband buying Milky Ways. By clue 14, the Kruegers live next door to the couple whose husband is masquerading as Capt. Kirk. If John and his wife were the Kruegers, the husband going as Capt. Kirk would be doling out Milky Way candy bars--no (22). If Alice were Mrs. Krueger, John would be going as Capt. Kirk, another conflict with clue 22. So, the first alternative, that John and his wife bought the Twizzlers for Halloween, fails. If the woman going as Cinderella and her husband had decided on the Twizzlers as treats, with John and his wife then living on the other side of the couple giving away the Snickers in clue 3, either John or Alice would have to be living in the third inside house and would be giving out Whoppers. If Alice were giving out Whoppers, by clue 4, the couple giving out M & M's would have to live in the outside house next door to Alice and her husband, who would be the Myerses--no, Alice isn't Mrs. Myers (4). If John and his wife were giving out the Whoppers, Mr. Voorhees would be going as the Tin Man, and the Lechters would live in the outside house next to John (12). However, since Mr. Myers isn't John and the Myerses don't plan to give out the Twizzlers (19), there is no way for clue 4 to work given this arrangement. So, none of the possibilities for the couples giving out the Snickers and the Twizzlers to live next door to each other can work; those two couples live in 103 and 107 Elm St. or vice versa, with the couple giving away the Whoppers occupying 105 Elm (12). Since the wife going as Cinderella doesn't live at 101 or 109 Elm (6), by clue 3, she is giving away the Whoppers; and John and his wife have the outside home next to the couple giving out the Snickers bars. Alice isn't the wife masquerading as Cinderella (13), so by clue 8, Mrs. Voorhees is; and Alice and her husband live in the outside house next to the couple who bought Twizzlers as treats. By clue 2, the husband dressing as the Tin Man and his wife aren't providing Twizzlers; so, by clue 12, they are giving away the Snickers bars, the Lechters are giving out Twizzlers. By clue 4, then, John and his wife must have chosen M & M's for the trick or treaters, with Mr. & Mrs. Myers giving out Snickers. By elimination, Alice and her spouse are treating with Milky Ways. Since the Kruegers live next door to the man wearing the Capt. Kirk uniform and his wife (14), the Kruegers must be Alice and her husband; and Mr. Lechter is the Kirk afficionado. By elimination, John is Mr. Bates. The woman going as Florence Nightingale lives next door to the man dressing as Count Dracula (5), so Mrs. Bates can't be going as the famous nurse, nor can Alice Krueger. Mrs. Lechter also isn't the one going as Florence Nightingale (14), so Mrs. Myers is. Since John isn't wearing the Dracula getup (15), Mr. Voorhees is (5). By clue 16, John Bates plans to dress as Frankenstein's Monster, with Krueger then going as Darth Vader. By clue 7, Tina and her husband live next door to (between) Keith and his wife and Karen and her husband. Since Karen's husband isn't going as Frankenstein's Monster (7), Tina can't be Mrs. Myers. Since Alice and Keith aren't a couple (13), Tina can't be Mrs. Lechter. Tina is Mrs. Voorhees. Keith isn't masquerading as Capt. Kirk (9); so by clue 7, Keith is dressing as the Tin Man, and Karen is Mrs. Lechter. David isn't Krueger or Voorhees (17); he is Mr. Lechter. Bob is Voorhees (20) and Ray Krueger is giving out Milky Ways. Neither Mrs. Bates (10) nor Mrs. Krueger (21) is dressing as Raggedy Ann, so Karen Lechter is. By clue 16, Alice Krueger is going as Wonder Woman; so Mrs. Bates is dressing as a witch. Mrs. Bates is Mary, and Pamela is Mrs. Myers (18). Finally, John and Mary Bates live at 101 Elm St. (11), with the Myerses at 103, the Lechters at 107, and the Kruegers at 109. In sum, the five couples on Elm St. plan to greet the October 31st guests as follows:

  • 101 Elm St. -- John (Frankenstein's Monster) & Mary (Witch) Bates, M & M's
  • 103 Elm St. -- Keith (Tin Man) & Pamela (Florence Nightingale) Myers, Snickers
  • 105 Elm St. -- Bob (Count Dracula) & Tina (Cinderella) Voorhees, Whoppers
  • 107 Elm St. -- David (Capt. Kirk) & Karen (Raggedy Ann) Lechter, Twizzlers
  • 109 Elm St. -- Ray (Darth Vader) & Alice (Wonder Woman) Krueger, Milky Ways

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