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At this year's International English Spelling Bee For 10 Year Olds, the contest came down to four children. The judges decided to give each child two words to spell. No two children were given the same two words and each word was given to exactly two children. Each child was given a single attempt to spell each of their two words correctly. After all 8 spelling attempts, each word had been spelled correctly exactly once. The children received scores calculated as the length of the word multiplied by if they got the word correct (1) or incorrect (0), with the scores from their two words added together. The scores were:

1st received 22pts

2nd received 11pts

3rd received 10pts

4th received 0pts

Can you determine the placement each child received, and what each of the first and second words given to each child were?

Clues

  1. The four children are: The child who was given both words that start with 'U', The child who was given both words that start with 'P', the child who was given both words that end in 'esce', and Johan.
  2. Both of the children who were given the word 'Phosphoresce' spelled at least one of their words correctly.
  3. Exactly one of these two statements is true. Anna got first place, Natalia spelled 'Unconscious' incorrectly, and the person who placed in third was given the word 'Precocious' as their second word. Calvin spelled 'Phosphoresce' correctly, Johan spelled his first word correctly, and Anna's first word was 'Phosphoresce'. The grammar is correct. Both statements include 3 parts.
  4. The first word given to the person who came in first was the second word given to the person who came in fourth.

Potential assumptions: If a clue tells you that a child spelled a word incorrectly, you can assume that it means the word was one of the two words given to the child. The opposite of a child spelling a word correctly is that the word was spelled incorrectly, not that the child did not receive the word.

Also, as this is a logic grid puzzle, I just want to point out for anyone else who wants to try solving this, each word is used once as the first word given, and once as the second word given. If a solution would create the same word being used as the first word given to two different children, the solution is incorrect.

Logic Grid

I like making logic puzzles. Along with your answers I'm curious to know what you enjoyed about this puzzle, and how I could improve. Thanks!

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1 Answer 1

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From the preamble and the scores, we know:

  • 1st place spelled Phosphoresce and one of the ten-letter words correctly,
  • 2nd place spelled Unconscious correctly,
  • 3rd place spelled the other ten-letter word correctly.

  • Using the preamble and clue (1), we know Johan got Precocious and Unconscious (because every word must be used twice in total).

    That gives us the following pairs of words (unordered):

             Uncoalesce
             Unconscious
    
             Phosphoresce
             Precocious
    
             Phosphoresce
             Uncoalesce
    
     Johan   Precocious
             Unconscious

    Clue (2):
    Phosphoresce is paired with Precocious and Uncoalesce, which are the two ten-letter words.
    One of these pairs were both spelled correctly for 1st place, and the child with the other pair must have spelled the ten-letter word only for 3rd place.
    And that means 2nd and 4th place are the other two pairs ("both U" and Johan), both of whom must have spelled their ten-letter word wrong.

             Uncoalesce   (wrong)    2/4
             Unconscious
    
             Phosphoresce            1/3
             Precocious   (correct)
    
             Phosphoresce            1/3
             Uncoalesce   (correct)
    
     Johan   Precocious   (wrong)    2/4
             Unconscious

    Now on to clue (3):
    If the first sentence is true, Natalia was the other child with Unconscious and spelled it wrong so must be 4th, making Johan 2nd.

    If the second sentence is true, Anna and Calvin both got Phosphoresce so are 1st and 3rd in some order.
    That makes Natalia and Johan 2nd and 4th; and as Johan spelled a word correctly, they must be 2nd.

    So in either case we know Johan was 2nd and Natalia was 4th:

     Natalia Uncoalesce   (wrong)    4th
             Unconscious  (wrong)
    
             Phosphoresce            1/3
             Precocious   (correct)
    
             Phosphoresce            1/3
             Uncoalesce   (correct)
    
     Johan   Precocious   (wrong)    2nd
             Unconscious  (correct)

    From clue (4):
    1st place cannot share Phosphoresce with 4th place (Natalia), so must share their ten-letter word.

    So we know Uncoalesce is 1st place's first word, and Natalia's second.

     Natalia 2.Uncoalesce   (wrong)    4th
             1.Unconscious  (wrong)
    
               Phosphoresce (wrong)    3rd
               Precocious   (correct)
    
             2.Phosphoresce (correct)  1st
             1.Uncoalesce   (correct)
    
     Johan     Precocious   (wrong)    2nd
               Unconscious  (correct)

    Back to clue (3):
    If the second sentence is true, Calvin spelled Phosphoresce correctly so is in 1st place, so Anna is 3rd.
    Then Anna's first word is Phosphoresce, and Johan's first word is unconscious.

    But that would mean Natalia and Johan both have Unconscious as their first word, and (not explicitly stated, but clear from the grid) each word must appear once each as a first/second word.

    So the first sentence must be true, Anna was in 1st place, so Calvin got 3rd place with Precocious as his second word.

    And finally, Johan must have spelled Precocious first and Unconscious second to ensure each word appears once in each round.

     Natalia 2.Uncoalesce   (wrong)    4th
             1.Unconscious  (wrong)
    
     Calvin  1.Phosphoresce (wrong)    3rd
             2.Precocious   (correct)
    
     Anna    2.Phosphoresce (correct)  1st
             1.Uncoalesce   (correct)
    
     Johan   1.Precocious   (wrong)    2nd
             2.Unconscious  (correct)

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    • $\begingroup$ Seems like only one of those give a complete solution? $\endgroup$
      – justhalf
      Commented Feb 7 at 14:14
    • $\begingroup$ You got it. You just.made 1 mistake at the end. Each word is only use once as the first word given. Look at Johans and Natalias first words in your second solution. That makes your first solution the only correct one. Nice job! $\endgroup$
      – Truej
      Commented Feb 7 at 15:47
    • $\begingroup$ @Truej I'm probably missing something, but I've just re-read everything and I can't see that requirement stated anywhere. $\endgroup$
      – fljx
      Commented Feb 7 at 16:35
    • $\begingroup$ It's a logic grid. That's pretty standard. If you put your answers into the logic grid given you'll see the solution. $\endgroup$
      – Truej
      Commented Feb 7 at 17:00
    • $\begingroup$ @TrueJ Ah, I didn't really look at the grid. I just copied the words into a text editor, and solved it there. I'll update. $\endgroup$
      – fljx
      Commented Feb 8 at 9:23

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