BrainBashers Derby - Logic Puzzles
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?
Puzzle Copyright © Kevin Stone
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Answer
Taylor Tripton won with Midday Night.
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.
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) – so this must be the correct answer.
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