Question: Solving multiple equations at once for Shidoku

Im trying to create a groebner basis to solve a series of equations to make a basis. The values can only be 1 to 4 for a..p which im also unsure if/how to define which may be causing the problem.

 My equations are as follows:

e1 := (((a-1)(a-2))(a-3))(a-4) = 0;
e2 := (((b-1)(b-2))(b-3))(b-4) = 0;
e3 := (((c-1)(c-2))(c-3))(c-4) = 0;
e4 := (((d-1)(d-2))(d-3))(d-4) = 0;
e5 := (((e-1)(e-2))(e-3))(e-4) = 0;
e6 := (((f-1)(f-2))(f-3))(f-4) = 0;
e7 := (((g-1)(g-2))(g-3))(g-4) = 0;
e8 := (((h-1)(h-2))(h-3))(h-4) = 0;
e9 := (((i-1)(i-2))(i-3))(i-4) = 0;
e10 := (((j-1)(j-2))(j-3))(j-4) = 0;
e11 := (((k-1)(k-2))(k-3))(k-4) = 0;
e12 := (((l-1)(l-2))(l-3))(l-4) = 0;
e13 := (((m-1)(m-2))(m-3))(m-4) = 0;
e14 := (((-1+n)(n-2))(n-3))(n-4) = 0;
e15 := (((-1+o)(o-2))(o-3))(o-4) = 0;
e16 := (((p-1)(p-2))(p-3))(p-4) = 0;
e17 := a+b+c+d-10 = 0;
e18 := a*b*c*d-24 = 0;
e19 := e+f+g+h-10 = 0;
e20 := e*f*g*h-24 = 0;
e21 := i+j+k+l-10 = 0;
e22 := i*j*k*l = 24;
e23 := m+n+o+p-10 = 0;
e24 := m*n*o*p-24 = 0;
e25 := a+b+e+f-10 = 0;
e26 := a*b*e*f-24 = 0;
e27 := c+d+g+h-10 = 0;
e28 := c*d*g*h-24 = 0;
e29 := i+j+m+n-10 = 0;
e30 := i*j*m*n-24 = 0;
e31 := k+l+o+p-10 = 0;
e32 := k*l*o*p-24 = 0;
e33 := a+e+i+m-10 = 0;
e34 := a*e*i*m-24 = 0;
e35 := b+f+j+n-10 = 0;
e36 := b*f*j*n-24 = 0;
e37 := c+g+k+o-10 = 0;
e38 := c*g*k*o-24 = 0;
e39 := d+h+l+p-10 = 0;
e40 := d*h*l*p-24 = 0;
e41 := c = 4;
e42 := e = 1;
e43 := j = 2;                  
e44 := p = 3;