A Puzzle of Shopping Perplexity

Two ladies went into a shop where, through some curious eccentricity, no change was given, and made purchases amounting together to less than five shillings.

“Do you know,” said one lady, “I find I shall require no fewer than six current coins of the realm to pay for what I have bought.”

The other lady considered a moment, and then exclaimed: “By a peculiar coincidence, I am exactly in the same dilemma.” “Then we will pay the two bills together.”

But, to their astonishment, they still required six coins.

What is the smallest possible amount of their purchases—both different?

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