| By clue 2, Cerise spent twice as much as the girl who bought a scarf;
while by clue 6, Dina spent twice as much as the girl who bought a gift
to give to Beth. Either four different girls are named between the two
clues or there is overlap: Cerise bought a gift to give to Beth or
Dina purchased a scarf. In case of either overlap, given that the
five spent a total of $210 with the least amount spent being $25 (clue 1),
we would get three purchases of $25, $50, and $100--leaving $35 between
the other two gifts and meaning at least one girl would have spent less
than $25. So, between clues 2 and 6, four of the five are named: Cerise
spent twice as much as the girl who bought a scarf, and Dina spent twice
as much as the girl who bought a gift to give to Beth. By clue 5, the
friend who purchased a necklace spent $15 more than Beth, who spent $5
more than the girl who bought a belt. So, Beth is either the girl who
bought a scarf in clues 2 and 6 or is the fifth girl to the four named
in those two clues. If Beth were the fifth girl to the four named in
clues 2 and 6, the belt would have been bought by Cerise or Dina or the
belt would have been bought as a gift for Beth. If Cerise had bought
the belt, given the minimum of $25 (1), the scarf would have cost at
least $25, Cerise would have spent at least $50 on the belt (2), Beth
would have spent $55, and the necklace would have cost $70 (5)--a total
of $200, leaving $10 for the fifth gift and contradicting clue 1.
If Dina had bought the belt, the gift for Beth would have cost at least
$25 (1), Dina would have spent at least $50 on the belt (6), Beth
would have spent $55, and the necklace would have cost $70 (5)--again a
total of $200, leaving $10 for the fifth gift and contradicting clue 1.
So, if Beth were the fifth girl, the belt would have been bought as a
gift for Beth. Dina then couldn't have bought the necklace in clue 5,
since clues 5 and 6 would work only if Dina spent $40 and the belt cost
$20. Cerise would have purchased the necklace. Either the scarf in
clue 2 or the belt for Beth in clue 6 would have cost the low of $25.
If the scarf cost $25, Cerise would have paid $50 for the necklace (2),
Beth would have spent $35, the belt would have cost $30 (5), and Dina
would have spent $60 (6)--a total of $200 and a conflict with clue 1.
If the belt for Beth had cost $25, Dina would have spent $50 (6), Beth
would have spent $30, Cerise would have paid $45 for the necklace (5),
and the scarf would have cost $22.50 (2)--no (1). Therefore, Beth in
clue 5 is not the fifth girl to the four in clues 2 and 6; Beth bought a
scarf. By clue 5, then, Cerise did not buy the necklace or from clues
2 and 5 she would have spent $30 and Beth $15. If the necklace were
bought to give to Beth, then given that the belt would have cost at least
$25, Beth would have spent at least $30, the necklace for Beth would
have cost at least $45 (5), Dina would have spent at least $90 (6), and
Cerise would have spent at least $60--a total of $250, no (1). If Dina
had bought the necklace, the belt wouldn't have been for Beth or Dina
would have spent $40 and the belt would have cost $20 (5, 6). If Dina
had bought the necklace, the belt wouldn't have been Cerise's purchase
or she would have spent less than Beth did on a scarf (2, 5). If Dina
had bought the necklace, the belt would have been purchased by the fifth
girl. She wouldn't have spent the low of $25, or Dina would have spent
$45 on the necklace (5) and the gift for Beth would have cost $22.50 (6),
too little. The gift for Beth would have cost $25, Dina would have paid
$50 for the necklace (6), Beth would have spent $35 on the scarf and
the belt would have cost $30 (5), and Cerise would have spent $70 (2).
By clue 7, however, the gloves cost neither the most nor the least and
cannot fit into this arrangement. Therefore, the necklace was the gift
bought by the fifth girl to the three in clues 2 and 6. Then either the
scarf Beth bought or the gift for Beth cost the $25. If the scarf
cost $25, however, the belt would have cost $20 (5)--no (1). So, the
gift for Beth cost $25, with Dina spending $50 (6). Cerise didn't buy
the belt since she spent more than Beth (2, 5). If Dina had bought the
belt, Beth would have spent $55, the necklace would have cost $70 (5),
and Cerise would have spent $110 (2)--a total of $310, no (1). The belt
is the gift for Beth. Then the necklace cost $45 and the scarf Beth
purchased cost $30 (5), with Cerise spending $60 (2). Erin purchased
the belt and Ally the necklace (3). By clue 7, the gloves were Dina's
purchase, with Cerise buying a gift for Erin--by elimination, a purse.
By clue 4, Beth bought a gift for Ally. Ally's purchase is for Dina
and Dina's for Cerise. In sum, the five friends purchased gifts at
Philene's Basement as follows:
- Cerise spent $60 on a purse for Erin
- Dina spent $50 on gloves for Cerise
- Ally spent $45 on a necklace for Dina
- Beth spent $30 on a scarf for Ally
- Erin spent $25 on a belt for Beth
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