BrainBashers - Random Puzzles

Puzzle 681

Can you add two lines to complete this sequence of towers?

5 towers with roofs: v-shaped+spire, v-shaped, double-v shaped, v-shaped, u-shaped.

Note: this puzzle is not interactive, and cannot be clicked.

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Puzzle 682

Chess Contestall 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?

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Answer
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 2^nd in croquet.
Name    Age    Chess  Croquet
Dale
Emery
Frankie               2
Glen

By (2), Dale came 3^rd 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 4^th in chess, came 3^rd in croquet, and by (7), they are 19. This can't be Dale (3^rd in chess), or Frankie (2^nd 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 4^th in croquet, so must be 1^st. Leaving Emery in 4^th.
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 4^th in both (as Glen is already 4^th in chess), so must be Frank, 2^nd in both. Leaving Emery 1^st 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

Puzzle 683

What comes next in this sequence:

Dave · Edward · Duncan · Neil · Liam · ?
Choose from:

Alan, Kevin, John, Michael, Steve

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Puzzle 684

Can you draw a continuous line that goes through every number in order, starting with 1, and ending with 6?

You can only move horizontally and vertically, every square must be visited, and the line must not cross itself.

...3../4...1./....../.6.5../2...../......

Note: this puzzle is not interactive, and the numbers cannot be clicked.

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