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 away--no, by the introduction. If the incident with the bath were in Near Yarrow, Large Manor would have to be 20 miles from Faxmouth--but 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 6-9 and the house with the hidden room 12-18 miles from Faxmouth; any other distances would put one or the other of those two houses outside the 5-20 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 Crumpet--no. 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 Cawfield-on-the-Rye 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:
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