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 70
Here we have a rectangular room, measuring 30 feet by 12 feet, and 12 feet high.
There is a spider in the middle of one of the end walls, 1 foot from the ceiling (A).
There is a fly in the middle of the opposite wall, 1 foot from the floor (B).
What is the shortest distance that the spider must crawl in order to reach the fly?
The Spider and the Fly, The Canterbury Puzzles, Henry Ernest Dudeney.
During the recent BrainBashers school sports day, four students were competing in the 400 metres hurdles.
Official figures mysteriously went missing just after the event, however, various spectators could remember the following information.
Alex won and wore red. The student wearing number 1 came third. Billie beat the student in yellow, but wasn't wearing number 2. Only one student finished in the same position as the number they wore, but they didn't wear red. Emery beat the student wearing number 3, and Glen wore yellow. The student in green wore number 2. A spectator remembered that one student wore blue, but couldn't remember anything else about them.
Can you determine the positions the students finished in, along with the numbers and colours they wore?
Answer # Name Wore Colour
1 Alex 4 Red
2 Emery 2 Green
3 Billie 1 Blue
4 Glen 3 Yellow
Reasoning
(Clue 1) Alex won and wore Red. (Clue 5) Glen wore Yellow. (Clue 3) Billie wasn't wearing number 2, and (Clue 6) number 2 wore Green, so must be Emery. Leaving Billie in Blue. # Name Wore Colour
1 Alex Red
? Glen Yellow
? Emery 2 Green
? Billie Blue
(Clue 2) Emery didn't come 3rd, and Alex won, so (Clue 5) Emery can't have come last, so must have come 2nd. # Name Wore Colour
1 Alex Red
2 Emery 2 Green
? Glen Yellow
? Billie Blue
(Clue 3) Billie can't have been last, so came 3rd and (Clue 2) wore 1, leaving Glen in last place. # Name Wore Colour
1 Alex Red
2 Emery 2 Green
3 Billie 1 Blue
4 Glen Yellow
(Clue 5) Emery beat the student wearing 3, so Glen must have worn 3. Leaving Alex wearing 4. # Name Wore Colour
1 Alex 4 Red
2 Emery 2 Green
3 Billie 1 Blue
4 Glen 3 Yellow
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