THE SOLUTION:

Barry found a penny,
Carrie found a dime,
Harry found a nickel,
Larry found a half-dollar, and
Mary found a quarter.

First, off, 91 cents can only be represented by five coins using a combination of penny, nickel, dime, quarter, and half-dollar; so those are our denominations.

There are a few different ways to solve this puzzle… here’s one logic sequence:

Clue 1: Since Harry’s coin was worth 5 times as much as Mary’s, either (A), (B) or (C) is true:

(A) Harry had the penny AND Mary had the nickel
(B) Harry had the nickel AND Mary had the quarter
(C) Harry had the dime AND Mary had the half-dollar

Clue 2: Since Carrie’s coin was worth 10x as much as Barry’s, either (D) or (E) is true:

(D) Barry had the penny AND Carrie had the dime
(E) Barry had the nickel AND Carrie had the half-dollar

So we can assume the following:

Barry has either the penny or nickel.
Carrie has either the dime or half-dollar.
Harry has either the penny, nickel, or dime.
Mary has either the nickel, quarter, or half-dollar.
We don’t have any information for Larry yet.

Reviewing the clues, we can determine that (A) is not possible, because if (A) were true, then neither (D) nor (E) could be true, and we know that one of those IS true.

Likewise, we can determine that (E) is not possible, because if (E) were true, then neither (B) nor (C) could be true, and we know that one of those IS true.

Since (E) is not possible, (D) is true, meaning that Barry has the penny and Carrie the dime.

By elimination, the only coin left for Harry is the nickel, revealing that (B) must be true. That means that Mary has the quarter, leaving the half-dollar for Larry.

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