BrainBashers - Random Puzzles

Puzzle 5

Below is a grid which should contain girl's names. The missing letters for a particular column are listed at the top of that column. Can you 'drop' the missing letters in and complete the grid?

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Puzzle 6

Using all of the letters A to Z, each once only, complete these common words.
a-a-e --ave -uie- --gon p--ot vi-e- -ac-t --met b--ep -u-ge -lan- -ra-e bon--

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Puzzle 7

After a day picking strawberries, I ended up with a full basket, which is always nice.

I ate 5, and then gave Alex half of the remaining.

I ate another 3, and then gave Billie one third of the remaining.

I ate another 6, and then gave Charlie two thirds of the remaining.

I now had 34 strawberries left. How many did I start with?

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Puzzle 8

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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