After the local BrainBashers Horse Show, some friends were telling everyone who had won.
Unfortunately, the friends were having trouble remembering, and in the course of the afternoon, they changed their minds a number of times.
In summary, they made the following statements:
Andy said: Taylor Tripton won with Evening Sunrise. Alex Ambleton won with Morning Sunset. Frankie Flanton won with Evening Sunrise. Billie said: Sam Spinton won with Midday Night. Frankie Flanton won with Evening Sunrise. Taylor Tripton won with Morning Sunset. Chris said: Alex Ambleton won with Midday Night. Sam Spinton won with Midday Night. Sam Spinton won with Morning Sunset. Dale said: Alex Ambleton won with Evening Sunrise. Frankie Flanton won with Morning Sunset. Sam Spinton won with Midday Night.
However, none of the statements were fully true.
In fact, just six of the statements were exactly half true (either the person won, or the horse did), the rest were false.
Can you determine who won, and which horse they were showing?
Reasoning
Before we begin the reasoning, let's look at the hint: 'Could Alex Ambleton have won?'. There are three horses in the puzzle, and Alex Ambleton is stated to have won with all three of them. We know that none of the statements were fully true, so Alex couldn't have won otherwise one of the statements would have been fully true.
However, we don't need the hint to solve the puzzle.
By grouping the clues together, we have:
1. Frankie Flanton won with Morning Sunset.
2. Frankie Flanton won with Evening Sunrise.
3. Frankie Flanton won with Evening Sunrise.
4. Sam Spinton won with Midday Night.
5. Sam Spinton won with Midday Night.
6. Sam Spinton won with Midday Night.
7. Sam Spinton won with Morning Sunset.
8. Taylor Tripton won with Morning Sunset.
9. Taylor Tripton won with Evening Sunrise.
10. Alex Ambleton won with Midday Night.
11. Alex Ambleton won with Morning Sunset.
12. Alex Ambleton won with Evening Sunrise.
We know that none of these statements were fully true, so, we know that (for example) it wasn't Frankie Flanton with Morning Sunset.
We can create a grid of all the possibilities and place an X where we know that it can't have been that combination:
M-N
M-S
E-S
Frankie
X
X
Sam
X
X
Taylor
X
X
Alex
X
X
X
We now have an X for all but 3 possibilities, and we know that exactly 6 of the clues must be half true.
So …
… if it was Frankie Flanton with Midday Night then exactly 7 clues would be half true (clues 1, 2, 3, 4, 5, 6, 10).
… if it was Sam Spinton with Evening Sunrise then exactly 8 clues would be half true (clues 4, 5, 6, 7, 2, 3, 9, 12).
… if it was Taylor Tripton with Midday Night then exactly 6 clues would be half true (clues 8, 9, 4, 5, 6, 10), and this must be the correct answer.
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 3
Which is larger:
loaves in a dozen baker's dozenpoints in the highest snooker break
