My Little Sister Triangle Geometry Problem

triangle.py

# The objective was to find all possible triangles
# that can have the sum of their three sides sizes equal to 10.
# (We consider only integer side sizes).
#
# I'm not good at Maths, and it was no obvious to
# enumarate all solutions, so I just wrote a program
# to do it for me.
eq_solutions = []
problem_solutions = []
y = 10
for i in range(1,10):
    for j in range(1,10):
        for k in range(1,10):
            if i + j + k == 10:
                eq_solution = [i, j, k]
                eq_solution.sort()
                if not eq_solution in eq_solutions:
                    eq_solutions.append(eq_solution)
print(eq_solutions)

for eq_solution in eq_solutions:
    if eq_solution[0] + eq_solution[1] >= eq_solution[2]:
        print(eq_solution[0], eq_solution[1], eq_solution[2], 'Valid solution')
        problem_solutions.append(eq_solution)
    else:
        print(eq_solution[0], eq_solution[1], eq_solution[2],
            'Not a valid solutiom: A+B < C ; {0} < {1}'.format(
                eq_solution[0] + eq_solution[1],
                eq_solution[2]))


print('The solutions are', problem_solutions)