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Need help in determining the following proof.

(See attached file for full problem description)

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Thm 11.1.2 (the pigeonhole principle):

Suppose that f:X Y is a function between non-empty finite sets such that |X| > |Y|. Then f is not an injection, i.e. there exist distinct elements x1 and x2 E (epsilon) X such that f(x1) = f(x2).
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Let Y be the set of types of currencies as well as empty. Y={$1,$5,$10,$20,$50,$100,empty} and |Y|=7
We make a function f: X->Y, for ...

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