Five horses - 'FIRST', 'SECOND', 'THIRD', 'FOURTH' and 'FIFTH' ran in the race. (There were no ties.)
'FIRST' did not come first.
'SECOND' was neither first nor last.
'THIRD' came in one place after 'FIRST'.
'FOURTH' was not second.
'FIFTH' was two places below 'FOURTH'.
In what order did the horses finish?
FOURTH SECOND FIFTH FIRST THIRD
I used the following approach:
Let's say:
Fir= First
S= Second
T= Third
Fo= Fourth
Fif= Fifth
The outcome of the race will be:
____ ____ ____ ____ ____
FIRST did not come first, so:
____ ____ ____ ____ ____
------Fir---Fir---Fir---Fir
SECOND was neither first nor last.
____ ____ ____ ____ ____
-----Fir--Fir--Fir--Fir
-----S----S----S
THIRD came in one place after FIRST. (This means FIRST can't be last, for there is no place after last place.)
____ ____ ____ ____ ____
-----Fir--Fir--Fir
-----S----S----S
----------T----T----T
FOURTH was not second.
____ ____ ____ ____ ____
-----Fir--Fir--Fir
-----S----S----S
----------T----T----T
Fo--------Fo---Fo---Fo
Finally, FIFTH was two places below FOURTH (This means that FOURTH can't be 4th or last place, for there is no place 2 places after them.)
____ ____ ____ ____ ____
-----Fir--Fir--Fir
-----S----S----S
----------T----T----T
Fo--------Fo
----------Fif-------Fif
Because there is only one horse that could be first place (FOURTH), it must be first. Because we know where FOURTH is, we know where FIFTH is, which is 2 places after. No other horse can be in that place.
-Fo--____ Fif--____ ____
-----S---------S
-----Fir-------Fir
---------------T----T
FIRST cannot be 2nd place because THIRD has to be one place after FIRST, but 3rd place is already filled. So, FIRST but in the remaining spot, 4th. Thus, THIRD must be last.
-Fo--____ Fif--Fir--T
-----S
Because SECOND remains, it must be in the last spot.
Fo S Fif Fir T
FOURTH SECOND FIFTH FIRST THIRD
solution (same as sks) but diff approach
