After the recent BrainBashers annual marathon, the judges were comparing notes to determine who finished where. From their notes, can you help them reconstruct the final result?
Max Merrymood beat Toby Trent and Jesse Jackson. Pat Piper beat Jesse Jackson, Toby Trent, and Alex Ardle. Zeb Zebra lost to Pat Piper. Glenn Goodfellow beat Toby Trent Zeb Zebra beat Frankie Flint. Glenn Goodfellow lost to Frankie Flint and Pat Piper. Toby Trent beat Billie Brick. Alex Ardle beat Zeb Zebra, Kelly Kingfisher, and Glenn Goodfellow. Kelly Kingfisher lost to Glenn Goodfellow and Max Merrymood. Billie Brick beat Kelly Kingfisher. Max Merrymood lost to Alex Ardle and Zeb Zebra. Frankie Flint beat Toby Trent, Max Merrymood, and Billie Brick. Toby Trent lost to Jesse Jackson and Alex Ardle. Jesse Jackson beat Glenn Goodfellow and Billie Brick.
Hint
Try rewriting the clues so that those who finished ahead are written first.
Answer
Pat Piper (P)
Alex Ardle (A)
Zeb Zebra (Z)
Frankie Flint (F)
Max Merrymood (M)
Jesse Jackson (J)
Glenn Goodfellow (G)
Toby Trent (T)
Billie Brick (B)
Kelly Kingfisher (K)
Reasoning
If we number the clues, write each name using a single letter, and rewrite the clues so that those who finished ahead are written first:
M beat T and JP beat J, T, and AP beat ZG beat TZ beat FF and P beat GT beat BA beat Z, K, and GG and M beat KB beat KA and Z beat MF beat T, M, and BJ and A beat TJ beat G and B
By (2): P A
By (8): P A Z
By (5): P A Z F
By (12): P A Z F M
By (1): P A Z F M J
By (14): P A Z F M J G
By (4): P A Z F M J G T
By (7): P A Z F M J G T B
By (10): P A Z F M J G T B K
??
Puzzle 2
How many people must be at a party before you are likely to have two having the same birthday (but not necessarily the same year)?
Reasoning
By likely, we mean greater than 50% chance.
With one person there is a 0 percent chance that you'll have two people with the same birthday.
With two people the probability that they won't share a birthday is 364 ÷ 365. The probability that they will share a birthday is therefore 1 − (364 ÷ 365).
With three people the probability that they won't share a birthday is the same as for two people, times 363 ÷ 365. So the probability that three people will share a birthday is 1 − (364 ÷ 365) x (363 ÷ 365).
Notice that with each additional person added, the probability that they share a birthday with one of the previous persons goes up, because there are fewer "free" days remaining.
We keep adding people until the percentage is greater than 50%.
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 4
Can you find every occurrence of the word MARCH that appears in this grid (horizontally, vertically, or diagonally)?
The hint will reveal the number of times it occurs, but where are they?
Note: this puzzle is not interactive, and the letters cannot be selected.
