Puzzle 33
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 (i.e. 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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Hint
Could Alex Ambleton have won?
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 (e.g.) 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.
Puzzle 34
Below, 10 nine-letter words have been broken into chunks of three letters.
These chunks have been mixed up, no chunk is used twice and all chunks are used.
Can you determine what the 10 words are?
ely rec ant htn fer ort
ent cer por sin lig ian
lio row use rar lib ive
tfo sca ing ing far eth
som dif est dig imp mho
Puzzle Copyright © Kevin Stone
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Hint
These are the first letters of the words: D, D, F, I, L, L, P, S, S, S.
Answer
dif + fer + ent = different
dig + est + ive = digestive
far + mho + use = farmhouse
imp + ort + ant = important
lib + rar + ian = librarian
lig + htn + ing = lightning
por + tfo + lio = portfolio
sca + rec + row = scarecrow
sin + cer + ely = sincerely
som + eth + ing = something
Puzzle 35
This famous river has a number of cities along its course.
What is its name?
Puzzle Copyright © Lloyd King
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Share Link – www.brainbashers.com/puzzle/zyvt
Hint
The answer is in front of you.
Answer
Mississippi.
The diagram is actually the word "mississippi" on its side.
Puzzle 36
My local library decided to hand out some of its old books to the 1,400 people who lived in the town.
To each library member, they offered 6 books, and to each non-member, they offered 4 books.
If only half of the members, and three-quarters of the non-members, accepted the books, how many books were given away?
Puzzle Copyright © Kevin Stone
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Hint
As we don't know how of the people were library members, you can try a random number and see what happens.
Answer
4,200 books.
Reasoning
It doesn't matter how many library members there were, as 1/2 of them accepted the books, and each accepted 6 books, which is 3 books per member on average.
Similarly, it doesn't matter how many non-members there were as 3/4 of them accepted the books, and each accepted 4 books, which is again 3 books per non-member on average.
Double-Checking
Both the members and non-members accepted, on average, 3 books each.
And 1400 x 3 = 4200.
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