BrainBashers - Random Puzzles

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Puzzle 109

Below is a very special grid, around each shaded number are 8 white squares.

However, each white square should have a number from 1 to 7.

Once filled in, these 8 numbers will sum to the shaded number.

In addition, once completed correctly, no row nor column will contain a duplicate number within a white square.

For example, the top row may be 5 6 4 2 3 1 7, etc.

This is a very difficult puzzle, and many people resort to using a computer to help them, which is a challenge in itself.

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Puzzle 110

What is the next letter in this sequence:

Q · E · T · U · ?

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Puzzle 111

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 112

What number is …

… three-quarters of eight-ninths of one-half of 2001?

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