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When I met Megan the other day in Starpounds, she was not her usual calm self.

"Goodness, what a shake-up! Everyone shifted from one job to another..."

"The Cabinet reshuffle?"

"Blithering ramblers!" she replied, a bit annoyed.

"Yes, those politicians can go on a bit, sometimes."

"No, no. The Rambling Club. In Blithering." Blithering's a village just outside the city. "They had their AGM last week. Andy's taken over from Phil as chairman, but not only that -- nobody's got the same post as before."

"Nice to have some new blood on the committee."

"It would have been, perhaps, but the only people nominated for committee posts were the old committee, so all eight of them just moved from one post to another, everyone getting replaced by a second person in their old post and taking over from a third person in their new one."

"So who's who now, then?"

"Hang on, I made some notes..." Megan grabbed her large floppy shoulder-bag, and rummaged around in it for a while. "Oh, bummocks -- must've left 'em in my rucksack. Anyway...... Thingummy who was the Social Secretary has replaced thingy who's now the Event Organizer."

With a memory for names like this, piecing the information together would prove tricky.

"Trevor's replaced thingy, who's replaced wossname, who's got Elaine's old post. Jean's got replaced by... who was it now? Not Graham... he got some other job. And thingy who was the IT Secretary is now... the Programme Co-ordinator? No, that was someone else. The ex-Footpath Officer's replaced Christine, who's replaced the new General Secretary. And the ex-Treasurer's replaced Val, who's replaced the new Treasurer."

So who's replaced whom in which job? And if you're going to post your answer, please could you also show your deductions you used, to find it? For the sake of clarity: the eight committee posts are the same as they were before; none were vacant; none are now vacant; nobody had and nobody now has more than one post at the same time.

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I think the solution is: (in format: name - old position -> new position)

Andy - general secretary -> chairman
Phil - chairman -> footpath officer
Elaine - footpath officer -> programme coordinator
Christine - programme coordinator -> IT secretary
Trevor - IT secretary -> general secretary
Graham - treasurer -> event organizer
Val - event organizer -> social secretary
Jean - social secretary -> treasurer

Reasoning:

First, notice that

the ex-treasurer, Val and the new treasurer have taken over each other's post (in a cyclic way):
name1 - treasurer -> post1
Val - post1 -> post2
name2 - post2 -> treasurer

(in my notation, two posts with the same number must be identical, but differently numbered posts are not necessarily different; the same goes for the names)

we also know about

a replacement chain between the ex-footpath officer, Christine and the new general secretary:
name3 - footpath officer -> post3
Christine - post3 -> post4
name4 - post4 -> general secretary

and

another small chain around the chairman position:
Phil - chairman -> post5
Andy - post6 -> chairman

We should notice, that

this second chain cannot be contained in the cycle or in the other chain, so these are actually the 8 different people.

Hence

the two chains together must form a cycle, which makes Phil the new footpath officer, and Andy the ex-general secretary.

Next, we should use that

Trevor takes over name5's post, who takes over name6's post, who takes over Elaine's post.
This 'distance of 3 posts' between Trevor and Elaine is only possible in the longer cycle: Trevor is the new general secretary, and Elaine is the ex-footpath officer.
(In other words: Trevor cannot be in the place of name1 above, because that would make Elaine in the same place. The same stands for name2. If Trevor was in name3's place, then there was a conflict between Elaine and Andy being the ex-general secretary. So Trevor can only be in the place of name4.)

Knowing that

Graham did not replace Jean, but we only have these two names left for the ex-treasurer and the new treasurer, it must be Jean who replaced Graham as treasurer.

Now, we know, that

the ex-social secretary took over the (ex-)post of the (new) event organizer. So these two posts have a distance of 2. The only people who we don't know yet their new posts are Elaine, Christine, Graham and Val. Only Graham and Val have a distance of 2, so Graham has to be the new event organizer (taking over from Val), and Val is the new social secretary (replacing Jean).
(In other words: to whom could the ex-social secretary post belong (the possibilities being Christine, Trevor, Val and Jean, we already know the ex-posts of the others)? It cannot be Christine, because that would make Trevor the new event organizer and the new general secretary at the same time. Also it cannot be Trevor, because then Andy would have a conflict between new posts of chairman and event organizer. It cannot be Val either, because then Jean would have a conflict between the treasurer and event organizer in her new position. So it must be Jean, making Graham the new event organizer.)

Finally, Megan mentioned, that

the ex-IT secretary did not become programme coordinator, but we also know these two are Christine's old and new posts. So it must have been the other way around: Christine becomes IT secretary (instead of Trevor), and is taken over in her programme coordinator post by Elaine.

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  • $\begingroup$ Youve started with what I, too, thought was the most helpful clue. Well spotted! $\endgroup$ – Rosie F Jul 19 '16 at 8:11
  • $\begingroup$ I think the key was to recognize that the first 8 lines I listed are about 8 different people. Then the rest is just trying to find information which only fit into one place into that skeleton. $\endgroup$ – elias Jul 21 '16 at 19:21

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