Logic Problem Solution:
Syd Slapdash and the Great Houses of Gloucester
From the introduction, the distance going west from Faxmouth to
Pencester is 25 miles, and the great houses of Gloucester are in
villages each at a different whole mile distance from the two towns.
By clue 8, the house closest to Faxmouth is 5 miles away, and the
house farthest from Faxmouth is 20 miles away. By clue 1, the great
house in Upper Crumpet is twice as far from Faxmouth as Mortar
Castle. By clue 5, Upper Crumpet is closer to Faxmouth than to
Pencester. Therefore, Upper Crumpet is 12 miles or less from
Faxmouth; and by clue 8, Upper Crumpet is either 10 or 12 miles
from Faxmouth with Mortar Castle then 5 or 6. If Upper Crumpet
were 12 miles from Faxmouth, Mortar Castle were 6, a third great
house of Gloucester is 20, and a fourth 5 (8), by clue 4, the house
where Syd Slapdash got stuck in the hidden room is twice as far from
Faxmouth as Highhopes House. Highhopes House couldn't be in Upper
Crumpet, or the house with the hidden room would be 24 miles from
Faxmouth. So, given the distances of 5, 6, 12, and 20 miles,
either Highhopes House would be 5 miles from Faxmouth and the house
with the hidden room 10, or the house with the hidden room would be
20 and Highhopes House 10; any other distance for Highhopes House
would make six houses. In either case, the fifth house would
be 10 miles from Faxmouth. However, there is no way for clue 10
to work given this arrangement. Therefore, Upper Crumpet is 10
miles from Faxmouth, Mortar Castle is 5, and a third great house
is 20 (8). By clue 4, either Highhopes House is in Upper Crumpet
and the house with the hidden room is 20 miles from Faxmouth, or
the two houses in the clue are the fourth and fifth to the three
already found. Trying the first case, since the house in Near
Yarrow isn't where Syd got stuck in the hidden room (9), by clue
6 the fourth and fifth houses would be the one in Near Yarrow and
the one where Syd got cornered by the foxhounds. By clue 2, Syd
would have knocked over the suit of armor in Buncombe Heath at
Mortar Castle. The incident with the Major's bath (10) couldn't
have been in Upper Crumpet, or Large Manor would have been where
the foxhounds disaster occurred and Near Yarrow would then be 22
miles from Faxmouth (10, 6) or Large Manor would have been in Near
Yarrow 11 miles from Faxmouth (10), with the house where Syd got
among the foxhounds then 5 and 1/2 miles awayno, by the
introduction. If the incident with the bath were in Near Yarrow,
Large Manor would have to be 20 miles from Faxmouthbut Near
Yarrow would then be 19 and the house where the foxhounds incident
happened would be 9 1/2. So, Highhopes House is not in Upper
Crumpet. In clue 4, Highhopes House and the house where Syd got
locked in the hidden room are the fourth and fifth houses; also,
Highhopes House must be 69 and the house with the hidden room 1218
miles from Faxmouth; any other distances would put one or the other
of those two houses outside the 520 mile range given in clue 8. By
clue 6, the house in Near Yarrow is twice as far from Faxmouth as the
house where Syd got into the foxhounds' pen. The house in Near
Yarrow isn't where Syd got stuck in the hidden room (9). Since no
two villages are the same distance from Faxmouth (intro), the house
in Near Yarrow can't be Highhopes House because the foxhounds incident
would have occurred at Mortar Castle and Near Yarrow would be 10
miles from Faxmouth, the same as Upper Crumpet. Therefore, the house
in Near Yarrow is the one 20 miles from Faxmouth, and Syd Slapdash
encountered the foxhounds in Upper Crumpet. By clue 10, Large Manor
can't be where the secret room is, since the Major's bath incident
would then have been at the house in Upper Crumpetno. Large Manor
is in Upper Crumpet, so the house where Syd walked in on the Major
in his bath is 9 miles from Faxmouth and must be Highhopes
House, with the house with the secret room then 18 miles out (4).
By clue 2, Syd knocked over the armor at Mortar Castle in Buncombe
Heath. By elimination, he mistook the Earl for a gardener in the
Near Yarrow visit. Then the house in Near Yarrow is Red Grange
and the one with the secret room is Waterloo Palace (3). By clue 7,
Waterloo Palace is in CawfieldontheRye and Highhopes House in
Great Minton. Syd Slapdash's mad tour of the great houses of
Gloucester went from incident to incident on the trip from Faxmouth
to Pencester as follows:
 5 miles, Mortar Castle in Buncombe Heath, knocked over the suit of armor
 9 miles, Highhopes House in Great Minton, walked in on Major Marple's bath
 10 miles, Large Manor in Upper Crumpet, wandered into the foxhounds' pen
 18 miles, Waterloo Palace in CawfieldontheRye, got locked in the secret room
 20 miles, Red Grange in Near Yarrow, mistook the Earl for a gardener

