During a recent expedition, three intrepid adventurers were left stranded in the middle of the desert with only a crate full of apples.
During the night, Alex woke up and decided to hide some of the apples and hid a third, then promptly fell asleep again.
Billie woke up shortly after and also decided to hide a third of the remaining apples and then also dozed back to sleep.
Finally, Charlie woke up and seeing the others were asleep, took a third of what was left.
Of course, none of the adventurers knew of the other's antics, so, in the morning, they shared the remaining apples, each receiving sixteen. How many apples were in the crate originally?
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
