| By clue 1, the couple receiving the largest refund will be getting back twice
as much money from the IRS as the couple with the 2nd-biggest refund. Since
Keith and his wife will be receiving a refund of $1,500 (clue 8), the gap
between the largest two refunds must be at least $750. In clues 4 and 7,
then, given the $500 gap between their refunds and other refunds, neither
Lon and his wife nor Mark and his will be getting the most
back; so, in those two clues, either Mark and his wife get the 2nd- and
Lon and his wife the 3rd-biggest income tax refund or vice versa. If Mark
and his wife were getting the 2nd- and Lon and his wife the 3rd-largest
refunds, by clue 4, Ellen and her husband would be getting the 4th-most money
back and the Rodmans would be getting the 5th-most. By clue 7, with Mark
and his wife getting the 2nd-biggest refund, Mrs. Truman couldn't be Ellen
or both Mark and his wife and Lon and his would be getting the same refund
(4, 7)--no, by the introduction. Mr. Truman would have to be Lon, or there
would be more than five couples. Then Debra in clue 7 would have to be
Mrs. Rodman in clue 4 or there would be more than five couples. However,
the gap between Lon and his wife and Debra Rodman and her husband would be
$1,500 in clue 4 and $500 in clue 7. Therefore, Lon and his wife are
getting the 2nd- and Mark and his wife the 3rd-largest refunds. By clue 7,
the 4th-most money back is to the Trumans and the 5th-most to Debra and her
husband. Debra must be Mrs. Rodman in clue 4 or there would more than five
couples. Since both Ellen (4) and Mark (7) are recipients of $1,000 more
than Debra Rodman and her husband (4, 7), Ellen and Mark must be a couple since no
two are receiving the same amount back from the IRS. By clue 2, Ian is Mr.
Truman. If Keith and his wife's refund of $1,500 (8) were the largest,
Lon and his wife would be getting back $750 (1)--impossible, since in clue 4
the Rodmans would then owe money. So, Keith is Mr. Rodman, with Jeff and
his wife due the largest refund. Keith and Debra Rodman are getting $1,500
back (8), so the Trumans are getting $2,000 and Mark and Ellen $2,500 (7).
Lon Truman and his wife are due $3,000 (4), and Jeff and his wife will
receive a check for $6,000 (1). By clue 3, Lon is Mr. Paulman and Brenda
Mrs. Truman. Jeff's wife is Christie and Lon's is Alice (5). By clue 6, Jeff
and Christie are the Wymans, and Mark and Ellen are the Shermans. In sum, the
five last-minute couples are due income tax refunds as follows:
- Jeff & Christie Wyman, $6,000
- Lon & Alice Paulman, $3,000
- Mark & Ellen Sherman, $2,500
- Ian & Brenda Truman, $2,000
- Keith & Debra Rodman, $1,500
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