the base case for this problem is actually n = 6 and n = 7, not just n = 6. (you'll see why later!) now suppose that n > 7 and that the claim is true

for all then therefore: and the induction is complete!

Remark:as you may have noticed, for n > 6, the inequality is strict, i.e. it's a good exercise to try to find anon-inductivesolution as well!