The recent BrainBashers annual marathon has just taken place.
The judges have given up keeping track of who won, as the results go missing every year.
Using the following spectators' notes, can you determine who finished where?
Terry Tipton finished after Lake Linkerton and Alex Adams but before Mason Miller. Pat Peterson finished before Dale Dartford and Lake Linkerton. Ryan Richards finished after Pat Peterson and before Jesse Jacks and Harper Hall. Kelly Kirkpatrick finished after Pat Peterson, Mason Miller, and Terry Tipton. Lake Linkerton finished after Alex Adams and Dale Dartford but before Jesse Jacks and Mason Miller. Mason Miller finished after Ryan Richards and Alex Adams. Alex Adams finished before Jesse Jacks, Mason Miller, and Pat Peterson. Dale Dartford finished before Kelly Kirkpatrick and Terry Tipton but after Ryan Richards. Jesse Jacks finished before Kelly Kirkpatrick, Terry Tipton, and Mason Miller, but after Pat Peterson and Dale Dartford. Harper Hall finished before Mason Miller but after Lake Linkerton, Jesse Jacks, and Terry Tipton.
Answer
Alex Adams
Pat Peterson
Ryan Richards
Dale Dartford
Lake Linkerton
Jesse Jacks
Terry Tipton
Harper Hall
Mason Miller
Kelly Kirkpatrick
Reasoning
If we number the clues, write each name using two letters, and rewrite the clues so that those who finished ahead are written first:
LL and AA beat TTTT beat MMPP beat DD and LLPP beat RRRR beat JJ and HHPP, MM and TT all beat KKAA and DD beat LLLL beat JJ and MMRR and AA beat MMAA beat JJ, MM and PPDD beat KK and TTRR beat DDJJ beat KK, TT, MMPP and DD beat JJHH beat MMLL, JJ and TT all beat HH
By (10): AA PP
By (4): AA PP RR
By (12): AA PP RR DD
By (7): AA PP RR DD LL
By (8): AA PP RR DD LL JJ
By (13): AA PP RR DD LL JJ TT
By (16): AA PP RR DD LL JJ TT HH
By (15): AA PP RR DD LL JJ TT HH MM
By (6): AA PP RR DD LL JJ TT HH MM KK
?
Puzzle 200
Start with a number larger than 0, square it, add 4, double, take away 3, times 4 and finally subtract the original number.
If you were now left with 20, what number did you start with?
Reasoning
If we convert the question to algebra, we have:
((n^2 + 4) x 2 − 3) x 4 − n = 20
Expanding the brackets and simplifying gives:
(2n^2 + 8 − 3) x 4 − n = 20
(2n^2 + 5) x 4 − n = 20
8n^2 + 20 − n = 20
8n^2 − n = 0 (*)
8n − 1 = 0
8n = 1
n = 1/8
In the equation marked (*) zero is also a potential solution, but as the question tells us that we "Start with a number larger than 0" we know that n can't be 0, and therefore we can safely divide by n.
