Logic Problem Solution:
LastMinute Lester at the Beach
By clue 1, LastMinute Lester got a room at the Sand Dollar Motel the
night before staying in Full Moon Bay; and by clue 5, the family stayed
in Full Moon Bay the night before staying in a motel whose room cost
twice as much as the one in Full Moon Bay. By clue 3, the Beachcomber
Motel stay was the night before the stay in the room that cost $50 less
than the Beachcomber did and two nights before the overnight in Cape
June. So, there must be some overlap between the two sets of three
night stays: the Beachcomber can't be in Full Moon Bay, since clues
3 and 5 would conflict, so the two possibilities are that LastMinute
Lester found a room at the Beachcomber Motel for Sunday night and then
at the Sand Dollar in Cape June for Tuesday, or that Lester found the
room at the Sand Dollar on Sunday and at the Beachcomber on Tuesday.
Trying the first arrangement, by clue 6, Wednesday's room cost $100
more than Monday's did, so if we let X equal Monday's room cost,
Wednesday's in Full Moon Bay would be X + 100 and Sunday's at the
Beachcomber Motel would be X + 50 (3). Thursday's cost would
be 2X + 200 (5). By clue 2, Lester found a room in Atlantic
Palisades earlier in the week than when the family stayed at the Dolphin
Inn, which cost $100 less than the lodging in Atlantic Palisades. The
family then couldn't have stayed at the Dolphin Inn on Monday, since
the Sunday stay cost only $50 more than Monday's; nor could the family
have stayed at the Dolphin Inn on Wednesday or Thursday and in Atlantic
Palisades on Sunday or Monday, since both nights later in the week
would have cost more than either Sunday or Monday night. Therefore,
Lester found a room at the Sand Dollar on Sunday night, in Full Moon
Bay on Monday, at the Beachcomber Motel on Tuesday for twice as much
as the room in Full Moon Bay, on Wednesday for $50 less than what he
paid at the Beachcomber, and on Thursday night in Cape June. Letting
Monday's room cost equal X, Tuesday's would then be 2X
(5) and Wednesday's X + 100 (6). By clue 3, Wednesday's room
cost $50 less than Tuesday's, so X + 100 = 2X  50.
Solving, X = 150. So, Monday's room cost $150, Tuesday's was
$300, and Wednesday's was $250. By clue 2, if the Dolphin Inn were
Monday's stay, the Sand Dollar room would have cost $250, the same as
Wednesday's stopno (7). If the Dolphin Inn were Wednesday's lodging,
the Atlantic Palisades room would have cost $350 (2) and, by clue 7,
the lodging in Cape June would have cost $250the same as that in Full
Moon Bayand again no (7). Lester found a room at the Dolphin Inn
on Thursday night. If the Ebb Tide Hotel were Wednesday's lodging, the
room in Snug Harbor would have cost $350 (4) on Monday. But then, by
clue 7, the Dolphin Inn room would have cost $250, the same as the Ebb
Tide and a conflict with clue 7. So, Lester found a room at the Ebb
Tide Hotel on Monday and at the Isla del Sol Resort on Wednesday. By
clues 7 and 4, the Isla del Sol is in Snug Harbor. By clue 7, the
remaining two nights cost a total of $600. If Atlantic Palisades were
Sunday's stop, then between that lodging and the Dolphin Inn the $600
would have been split $350/$250 (2), the latter total being the same
as the Costa del Sol room and a contradiction with clue 7. So, Lester
found the room in Atlantic Palisades on Tuesday night for $300 and paid
$200 at the Dolphin Inn. By elimination, the family was in Ocean City
Sunday night and paid $400 for the room there (7). LastMinute Lester
found rooms at the beach as follows:
 Sunday  Sand Dollar Motel in Ocean City, $400
 Monday  Ebb Tide Hotel in Full Moon Bay, $150
 Tuesday  Beachcomber Motel in Atlantic Palisades, $300
 Wednesday  Isla del Sol Resort in Snug Harbor, $250
 Thursday  Dolphin Inn in Cape June, $200

