any vs every

[Seiichi Myoga]

I think since "any" in (1) means "every: every person or thing of a particular category or description, no matter who or what (Encarta)," we can replace "any" with "every."

(1) You can find a solution to any problem, no matter how big it may be.

Do you agree?

Thank you in advance
Seiichi MYOGA

Put differently, my interest is in what is your first choice ("any" or "every") when you rephrase a double-negative sentence like (i).

(i) No problem is so big that you can't find a solution to it.

[Jamie (K)]

My first choice is "any".