[Help-glpk] Can I use GLPK to solve this question?

[Sen-Lung Chen]

Dear All:
 I have a question about GLPK.Can I use GLPK to solve this question?
my question is show below.
I have some data
        1       0       1       1       0
        0       0       0       1       1
        1       1       0       0       1
        0       1       1       0       0
then I add another array X=[X0,X1,X2,X3,X4]
Now I must to select three column from data.

        x0      x1      x2      x3      x4
value   1       0       1       0       1
---------------------------------------------------------
pattern 1       0       1       1       0
        0       0       0       1       1
        1       1       0       0       1
        0       1       1       0       0

if the column is select, it's mapping item in X is 1,meanwhile,
the other item is 0 of unselect column.

My objective is to find the min length of unselect column,
for example, the unselected bit of the above case is x1 and x3
Y=[X1X3]=[01,10]


Another case:
        x0      x1      x2      x3      x4
value   0       1       1       0       1
--------------------------------------------------------------------
pattern 1       0       1       1       0
        0       0       0       1       1
        1       1       0       0       1
        0       1       1       0       0
Y=[x0x3]=[11,01,10,00]

the length of first case is 2, the second case is 4.
My objective is to find the minimum length.