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.
??
Puzzle 3
These five business people represented different companies at a recent trade fair. Unfortunately, the hotel they were all due to stay in had accidentally double booked their rooms. They tried other hotels in the area but all were fully booked. Consequently, they all agreed to share the only two rooms available in the hotel, one twin and one triple.
From the clues, can you work out each person's name, company and official title?
When the five realised their dilemma, they drew straws to see who would share with whom. The outcome for four of them was that the CEO shared with the business person from ABM Inc. and Glenn shared with the Developer. Alex does not work for Reed Right and is not the Director. The Director does not work for Lantel or Blue Teeth. Neither Clarkson nor Grimaldi works for Reed Right. Grimaldi is either the IT Analyst or the CEO. The business person from Reed Right did not share a room with Taylor. Clarkson, who does not work for Lantel, shared with either Taylor or Grimaldi but not both. Glenn's surname is either Casson or Graves. Glenn did not share with Charlie. The business person from Chiptech shared with the business person from Lantel. The CEO shared with the IT Analyst. Casson works for either Blue Teeth or Chiptech. Neither Jesse nor Alex works for ABM Inc. Fielder shared with the Director. The business person from Blue Teeth shared with the Developer.
First names : Alex, Charlie, Glenn, Jesse, Taylor.
Last names : Casson, Clarkson, Fielder, Graves, Grimaldi.
Company : ABM Inc., Blue Teeth, Chiptech, Lantel, Reed Right.
Position : Accountant, CEO, Developer, Director, IT Analyst.
Answer First Last Name Company Position Charlie Grimaldi ABM Inc. IT Analyst Glenn Casson Chiptech Director Jesse Graves Reed Right CEO Alex Clarkson Blue Teeth Accountant Taylor Fielder Lantel Developer
To solve this puzzle, you first need to determine who shared which room with whom. Three delegates shared the triple and two shared the twin. The CEO shared with the business person from ABM in one room and Glenn shared with the Developer in the other (1). Since Grimaldi is either the IT Analyst or the CEO (3) and the CEO shared with the IT Analyst, Grimaldi is in the same room as whoever is the CEO, IT Analyst and ABM delegate although Grimaldi could have been one of these people. Glenn did not share with Charlie (6) so Charlie is in the same bedroom as, and possibly is, the CEO, IT Analyst, Grimaldi and / or the ABM delegate. Grimaldi and Taylor were in different rooms so Taylor shared a room with Clarkson (5) and the Reed Right delegate was in a different room to Taylor. At this stage we know:
Room 1
CEO
IT Analyst
ABM delegate
Grimaldi
Charlie
Reed Right delegate
Room 2
Glenn
Developer
Taylor
Clarkson
Since the Chiptech delegate shared with the Lantel delegate (7), both of these must have been in room 2 otherwise there would be four delegates in room 1 which is not possible.
Now this has been ascertained, the puzzle can be solved:
The CEO shared with the IT Analyst so the IT Analyst must work for ABM (Clues 1 and 8) so the CEO must work for Reed Right. Since Grimaldi does not work for Reed Right, they must be the IT Analyst. Clarkson, Fielder and Casson are in room 2 so the CEO must be Graves. Graves is not Glenn (1), Taylor (4), Charlie (IT Analyst) or Alex (2) so must be Jesse. Clarkson is not Taylor (5), Glenn (6), Charlie or Jesse (in room 1) so must be Alex. The Director does not work for Lantel or Blue Teeth (2), Reed Right or ABM (room 1) so must work for Chiptech. This is not Graves or Grimaldi (room 1), Clarkson (2) or Fielder (11) so must be Casson. Since Graves' first name is Jesse, Casson must be Glenn (6). Alex Clarkson does not work for Reed Right or ABM (room 1), Lantel (5) or Chiptech so must work for Blue Teeth. Since they are not the Developer (12) they must be the Accountant. This leaves Taylor Fielder who is the Developer for Lantel.
???
Puzzle 4
In this long division, each number has been replaced by another. The answer has also been removed. Can you determine the answer?
....
———————
75 | 796767
791
——
57
30
——
86
82
——
47
47
——
9
