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 3
Can you add one Z to the following word to form another valid English word:
LEG
Hint
The fourth player is the key to this tricky question.
Answer
9 points.
Respectively the scores were 7, 14, 20, 30, 23, 9.
Reasoning
If we label the six players A, B, C, D, E, and F, we know that:
[1] A + B + C + D + E + F = 103
and from the clues:
A = B ÷ 2 B = C − 6 C = D x 2 ÷ 3 E = D − A F = E − 14
Note that it could be E = A − D or E = D − A, but using A − D we'd end up with a negative value for E later, which isn't allowed (so we'd have to try again with D − A anyway).
As we have no information for D, it's best to find all of the other letters in terms of D. These steps are left as an exercise (e.g. use C in the equation for B), but the result is:
A = ( D − 9) ÷ 3 B = (2D − 18) ÷ 3 C = (2D ) ÷ 3 D = (3D ) ÷ 3 E = (2D + 9) ÷ 3 F = (2D − 33) ÷ 3
Writing it as D = 3D ÷ 3 makes things slightly clearer in the next step.
