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Academic Decathlon 2004 Logic Quiz

Beach Party  (800 points)

Four mothers take their young children (two girls named Anita and Sheila, and two boys named Jeremy and Mark) for an outing at the beach.  Unfortunately each mother (including Susan) realized that she had forgotten a different crucial item of beach gear (one forgot her beach umbrella).  Luckily each had remembered to pack her child's sand pail (each of which has a different sea creature on it -- one pail has a seal design), so the other three mothers took turns watching the children play as, one  by one, each mother trudged home for the item she had forgotten.  From the following clues, can you match each mother with her child, the item she had forgotten, and the design on her child's sand pail?

1. The four mothers are Margaret, Anita's mom, the mother who forgot her paperback book, and the mother of the child with the dolphin pail.

2. The four children are Judy's daughter, Mark, the child with the octopus pail, and the one whose mother forgot her sunglasses.

3. The four items that were forgotten are the hat, the sunglasses, the item Margaret forgot, and the item that Jeremy's mother went to retrieve.

4. The four pails are the one with the octopus design, the one with the crab design, Anita's pail and the one carried by Ingrid's child.


Frankly, I don't know how to fill out the big chart.  Maybe if I did, I could do these puzzles more easily.

Here's how I solved it.

(5) Margaret's item isn't the paperback (clue 1) or the hat or sunglasses (clue 3) so Margaret forgot the beach umbrella.

(6) The child, Anita, doesn't have the dolphin pail (clue 1) or the octopus or crab pail (clue 4), so Anita's pail is the seal.

(7) Clue 3 tells you that Jeremy's mother didn't get the hat or sunglasses or the item Margaret forgot (beach umbrella, clue 5), so Jeremy's mother went back for the paperback.

(8) Ingrid's child's pail is not octopus or crab (clue 4), and Ingrid's daughter isn't Anita (clue 4), so Ingrid's child's pail is dolphin.

(9) Since Jeremy's mom forgot the paperback, and Ingrid's child has the dolphin pail, clue 1 says the four mothers are Margaret, Ingrid, Anita's mom, and Jeremy's mom.  So Anita's mom is Judy or Susan, and the other mom is Jeremy's, who forgot the paperback.  Clue 2 tells you that Judy's child is a girl, so it must be Anita; and so Susan's child must be Jeremy.

(10) Now we know that Susan forgot the paperback, Margaret forgot the beach umbrella, and clue 2 tells us Judy didn't forget the sunglasses, so Ingrid must have forgotten the sunglasses, and that leaves the hat for Judy to have forgotten.

(11) Clue 2 lists the children, one of whom is Mark.  Clue 2 eliminates Ingrid as a possible mother for Mark (because Ingrid forgot her sunglasses).  Judy's daughter is Anita, and Susan's son is Jeremy, so that leaves Margaret, who must be Mark's mom.  That leaves Sheila who must belong to Ingrid.

(12) Clue 2 lists Judy, Mark, and Ingrid (who forgot her sunglasses), so that leaves Susan/Jeremy whose pail must have the octopus design.  The only other design is the crab, which must belong to Margaret/Mark.

Mother Child Item Pail
Ingrid Sheila (11) sunglasses (10) dolphin (8)
Judy Anita (9) hat (10) seal (6,9)
Margaret Mark (11) beach umbrella (5)  crab (12)
Susan Jeremy (9) paperback (7,9) octopus (12)


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