# Puzzle ZIWD

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Chess Contest - Logic Puzzles

At the local games evening, four friends were competing in the chess and croquet competitions.

Frankie beat Glen in chess, Dale came third, and the 16-year-old won.
Frankie came second in croquet, the 15-year-old won, Dale beat the 18-year-old, and the 19-year-old came third.
Emery is 3 years younger than Glen.
The person who came last in chess came third in croquet, and only one person got the same position in both games.
Can you find the ages of the people and their positions in the two games?

Name    Age    Chess  Croquet
Dale    15     3      1
Emery   16     1      4
Frankie 18     2      2
Glen    19     4      3

Reasoning
The possible ages are: 15, 16, 18, 19.

Breaking the clues down, and numbering them:
Frankie beat Glen in chess. Dale came third (chess). The 16-year-old won (chess). Frankie came second in croquet. The 15-year-old won (croquet). Dale beat the 18-year-old (croquet). The 19-year-old came third (croquet). Emery is 3 years younger than Glen. The person who came last in chess came third in croquet. Only one person got the same position in both games.
By (4), Frankie came 2nd in croquet.
Name    Age    Chess  Croquet
Dale
Emery
Frankie               2
Glen

By (2), Dale came 3rd in chess.
Name    Age    Chess  Croquet
Dale           3
Emery
Frankie               2
Glen

By (8), Emery is 15 or 16, and Glen is 18 or 19.

By (9), the person who came 4th in chess, came 3rd in croquet, and by (7), they are 19. This can't be Dale (3rd in chess), or Frankie (2nd in croquet), or Emery (aged 15 or 16), so it must be Glen.
Name    Age    Chess  Croquet
Dale           3
Emery
Frankie               2
Glen    19     4      3

By (6), Dale can't have been 4th in croquet, so must be 1st. Leaving Emery in 4th.
Name    Age    Chess  Croquet
Dale           3      1
Emery                 4
Frankie               2
Glen    19     4      3

By (10), only one person got the same position in both games, this can't be Emery 4th in both (as Glen is already 4th in chess), so must be Frank, 2nd in both. Leaving Emery 1st in chess.
Name    Age    Chess  Croquet
Dale           3      1
Emery          1      4
Frankie        2      2
Glen    19     4      3

By (3) and (5) we know the ages of the winners in each competition, and Frankie is therefore 18.
Name    Age    Chess  Croquet
Dale    15     3      1
Emery   16     1      4
Frankie 18     2      2
Glen    19     4      3

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