How can the farmer catch the turkey?

Here is a pretty little game as well as a puzzle.  Place
a counter, supposed to be a turkey, on cell No. 7, and
another counter, to represent the farmer, on cell No. 58.
One player moves the turkey, the other player moves the
farmer.  They play alternately, moving their piece in any
direction in a streight line, as far as they please.  But
if a piece stops on a row guarded by the other man, or if
it passes over a row so guarded, it can be captured.  For
example, if the turkey moves first from cell 7 to cell 52,
it can immediately be captured by the farmer.  And if the
farmer moves first from 58 to 4, he can be captured by the
turkey at cell 12 because he crossed a row guarded by the
turkey.  The object of the game is to capture your opponent.
Regardless of who moves first, the farmer can always capture
the turkey.  What strategy should he follow in order to win?

For a second puzzle, start as before with the turkey on 7
and the farmer on 58.  The turkey does not move.  How can
the farmer capture it in twenty-four moves that take him
once and only once over every cell on the board?  It is
quite a difficult problem.
 
 
 
 
 
 

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                 THE SOLUTION
 

The farmer's strategy is to play to diagonally opposite
corners of squares until he forces the turkey to the border,
after which he wins easily.  If the farmer plays first, he
must move to cell 35.  There is no way the turkey can seize
the advantage because the spot between 9 and 10 is blank.
The following typical game should make the strategy clear:

          Turkey          Farmer

             8              50
            30              47
            29              46
            37              45
            29              38
            28              37
            51              29
            60              52 (wins)

The second puzzle is solved in twenty-four moves as follows:
52, 14, 15, 8, 9, 16, 18, 10, 11, 42, 39, 31, 33, 25, 22, 45,
50, 4, 4, 64, 60, 2, 3, 7.