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Breadth-first Searches (BFS) were both traditional & classical blind searching technique in artificial intelligence (AI). Variable Carrying Numbers (VCN) is a broad concept of numbers in number theory. AI-fuzzy VCN (IFN) is a mixture numbers with different Figures' Module (FM) in a same n-Figures number. Fixed Carrying Numbers (FCN) is only ones of special VCN. This paper makes an analyzing & discussing of BFS technology of both FCN and VCN in searching without information, and points out that, merits and demerits of two Numbers on searching without information. And then, it gives a novel IFN method of BFS in problem-solving which sometimes we should think simultaneously over the intelligent properties of VCN, and gives out an example of the problem-solving method, i.e. the problem-solving such as catching fish with casting a net or boy-herder picks peaches by climbing up a big tree.