BrainBashers - Random Puzzles

Puzzle 17

A 'complete' word is a word in which every letter, in turn, can be replaced by another to form a new word.

For example, RUG is a complete word because:
-ug = hug
r-g = rig
ru- = run

How many of the following words are not complete words? Proper nouns and names are not allowed.
team cost flew ward fail rook soft most lamp load

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Puzzle 18

Using the letters AAEEIIMMPPTT complete this grid. The grid reads the same across as down.

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

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Puzzle 19

What number comes next in this sequence:

31 30 31 31 ?
Clue: the answer is NOT 30!

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Puzzle 20

Pre-Championship Rehearsal – Logic Puzzles

At last month's rehearsal, four top athletes competed in two 400-metre qualifiers.

As the results were expected to be mislaid, various notes were taken to ensure the accuracy of the overall placings:

No one finished both races in the same position.
In both races, Sam beat the runner whose surname was Watson.
Billie Taylor came third in the second race, and Pat came last in the first race.
In the second race, the athlete whose surname was Arnold won, and the athlete whose surname was Bowler came last.
In the first race, Billie beat Jamie, but Jamie beat Sam.
Can you determine who finished where in each of the races?

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Answer
    Race1         Race2
————————————————————————
#1  Billie        Sam
    Taylor        Arnold
————————————————————————
#2  Jamie         Pat
    Bowler        Watson
————————————————————————
#3  Sam           Billie
    Arnold        Taylor
————————————————————————
#4  Pat           Jamie
    Watson        Bowler

Reasoning
The four names were: Billie, Jamie, Pat, Sam
The four contestants were: Arnold, Bowler, Taylor, Watson.

By (3), Billie Taylor came third in the second race, and Pat came last in the first race, giving:
    Race1         Race2
————————————————————————
#1

————————————————————————
#2

————————————————————————
#3                Billie
                  Taylor
————————————————————————
#4  Pat

By (5), in the first race Billie beat Jamie, and Jamie beat Sam, giving:
    Race1         Race2
————————————————————————
#1  Billie
    Taylor
————————————————————————
#2  Jamie

————————————————————————
#3  Sam           Billie
                  Taylor
————————————————————————
#4  Pat

By (2), Sam beat the runner with the surname Watson in the first race, which means that Pat's surname is Watson, giving:
    Race1         Race2
————————————————————————
#1  Billie
    Taylor
————————————————————————
#2  Jamie

————————————————————————
#3  Sam           Billie
                  Taylor
————————————————————————
#4  Pat
    Watson

By (1), Pat can't have also finished in last place in race 2, and by (2), Sam beat the Pat Watson, so Pat must have finished in second place in race 2. And Sam came first, therefore Jamie came last, giving:
    Race1         Race2
————————————————————————
#1  Billie        Sam
    Taylor
————————————————————————
#2  Jamie         Pat
                  Watson
————————————————————————
#3  Sam           Billie
                  Taylor
————————————————————————
#4  Pat           Jamie
    Watson

By (4), in the second race the athlete whose surname was Arnold won, and the athlete whose surname was Bowler came last, so we know Sam and Jamie's surnames, and we can complete the grid:
    Race1         Race2
————————————————————————
#1  Billie        Sam
    Taylor        Arnold
————————————————————————
#2  Jamie         Pat
    Bowler        Watson
————————————————————————
#3  Sam           Billie
    Arnold        Taylor
————————————————————————
#4  Pat           Jamie
    Watson        Bowler

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