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After the local BrainBashers Derby, some friends were telling everyone who had won.

Unfortunately, the friends were having problems with their memories and in the course of the evening they changed their minds a number of times.

In summary they made the following statements:

Alan said:
Steve Short won on Quick Cloud.
Tim Tiny won on Morning Sunset.
Dave Diddy won on Quick Cloud.

Brian said:
Simon Small won on Blue Paws.
Dave Diddy won on Quick Cloud.
Steve Short won on Morning Sunset.

Charles said:
Tim Tiny won on Blue Paws.
Simon Small won on Blue Paws.
Simon Small won on Morning Sunset.

Derek said:
Tim Tiny won on Quick Cloud.
Dave Diddy won on Morning Sunset.
Simon Small won on Blue Paws.

However, none of the statements were fully true.

In fact, only 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 riding?

Answer: Steve Short won on Blue Paws.

By grouping the clues together we have:

1 Dave Diddy won on Morning Sunset.
2 Dave Diddy won on Quick Cloud.
3 Dave Diddy won on Quick Cloud.

4 Simon Small won on Blue Paws.
5 Simon Small won on Blue Paws.
6 Simon Small won on Blue Paws.
7 Simon Small won on Morning Sunset.

8 Steve Short won on Morning Sunset.
9 Steve Short won on Quick Cloud.

10 Tim Tiny won on Blue Paws.
11 Tim Tiny won on Morning Sunset.
12 Tim Tiny won on Quick Cloud.

As none of these statements were fully true, setting up a grid helps and entering crosses for these clues allows us to eliminate them:
 Blue Paws Morning Sunset Quick Cloud Dave Diddy O X X Simon Small X X O Steve Short O X X Tim Tiny X X X
Which now only leaves three possibilities. We know that exactly 6 of the clues must be half true.

If it was Dave Diddy on Blue Paws then exactly 7 clues would be half true (clues 1, 2, 3, 4, 5, 6, 10).
If it was Simon Small on Quick Cloud then exactly 8 clues would be half true (clues 4, 5, 6, 7, 2, 3, 9, 12).
If it was Steve Short on Blue Paws then exactly 6 clues would be half true (clues 8, 9, 4, 5, 6, 10) - so this must be the correct answer. QED.

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