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Combinatorics Difficulty 3.0 AMC 10/12 Find the answer United Kingdom

Five children, Amy, Bob, Cat, Dan and Eve each make a statement about the number of pencils they have in their pencil case. Amy: "I have more than Bob." Bob: "I have more than Cat and more than Dan." Cat: "I have more than Dan." Dan: "I have more than Eve and more than Amy." Eve: "I have more than Amy." What is the largest number of these statements that can be true?

(A) $1$ (B) $2$ (C) $3$ (D) $4$ (E) $5$

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