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?
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
?
Puzzle 334
Using a tap, a container of 9 litres and a container of 4 litres …
Answer
Here are the contents of the containers after each stage:
A = 9 litres, B = 4 litres
A B
9 0 fill A
5 4 fill B from A (leaving 5 litres in A)
5 0 empty B
1 4 fill B from A (leaving 1 litre in A)
1 0 empty B
0 1 fill B from A
9 1 fill A
6 4 fill B from A (only 3 more litres fit in B)
6 0 empty B
The results of a recent Chess tournament between five close rivals is described below:
Dale finished before Alex. Emery finished after Bailey. Alex finished before Chris. Emery finished after Dale. Bailey finished before Alex. Dale finished after Bailey. Chris finished before Emery.
Who finished where?
Hint
Try rewriting each statement so that they are all 'finished before' statements instead.
Answer
Bailey won …
… then Dale, Alex, Chris, and Emery.
Reasoning
By placing the person who finished higher to the left, we have:
Dale finished before Alex (Dale > Alex)Emery finished after Bailey (Bailey > Emery)Alex finished before Chris (Alex > Chris)Emery finished after Dale (Dale > Emery)Bailey finished before Alex (Bailey > Alex)Dale finished after Bailey (Bailey > Dale)Chris finished before Emery (Chris > Emery)
From (1) and (3):
Dale > Alex > Chris
Adding (7):
Dale > Alex > Chris > Emery
Adding (6):
Bailey > Dale > Alex > Chris > Emery
Which is the final placing for all the players, and can be double-checked with the remaining clues.
