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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 Trigger.
   Tim Tiny won on Red Rum.
   Dave Diddy won on Trigger.

Brian said:
   Simon Small won on Black Beauty.
   Dave Diddy won on Trigger.
   Steve Short won on Red Rum.

Charlie said:
   Tim Tiny won on Black Beauty.
   Simon Small won on Black Beauty.
   Simon Small won on Red Rum.

Derek said:
   Tim Tiny won on Trigger.
   Dave Diddy won on Red Rum.
   Simon Small won on Black Beauty.

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?

 [Ref: ZXSC] © Kevin Stone

Steve Short won on Black Beauty.

By grouping the clues together we have:

1 Dave Diddy won on Red Rum.
2 Dave Diddy won on Trigger.
3 Dave Diddy won on Trigger.

4 Simon Small won on Black Beauty.
5 Simon Small won on Black Beauty.
6 Simon Small won on Black Beauty.
7 Simon Small won on Red Rum.

8 Steve Short won on Red Rum.
9 Steve Short won on Trigger.

10 Tim Tiny won on Black Beauty.
11 Tim Tiny won on Red Rum.
12 Tim Tiny won on Trigger.

As none of these statements were fully true, setting up a grid gives and entering crosses for these clues allows us to eliminate them:
 Black BeautyRed RumTrigger
Dave Diddy 
X
X
Simon Small
X
X
 
Steve Short 
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 Black Beauty then exactly 7 clues would be half true (clues 1, 2, 3, 4, 5, 6, 10).
If it was Simon Small on Trigger then exactly 8 clues would be half true (clues 4, 5, 6, 7, 2, 3, 9, 12).
If it was Steve Short on Black Beauty then exactly 6 clues would be half true (clues 8, 9, 4, 5, 6, 10) - so this must be the correct answer. QED.

Back to the puzzles...

 

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