Solved by Lu Richardson.

Solution
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The Dump

Rummage around the rubbish dump and get a shoe, a straight nail, a
broken flask and some whole flasks. You can come back here any time
and get some more of those (save the shoe, there is only one). By
the way, if you find an orange peel, use it on Malcolm for extra
points.

The Castle Gate

You could be dragged here at some point and taken to Prison, and
you'll return here afterwards. You can carry on from there. When
you get the scissors, cut both pennants for extra points. If you
don't get the scissors, a broken flask will do just as well.

The Prison

This sequence only appears to take place if you waste too much time
messing around. Follow the instructions precisely. The good thing
is that you get to keep the scissors; so towards the end, put them
in your inventory and don't leave them on the floor. However, as I
explain above, you don't really need them.

The Bluff

You can enter the machine at any time, which takes you to the Town
Center. Do so at least once to get the extra points.

Out of Town

You are after the mime's outfit. In order to get it, you have to
place an eel in the mime's hood; hang about till he turns around.
If he does not, the time is not yet - so go elsewhere. When you
succeed, he will go into the Baths. To follow him you need to have
tied the nut-on-a-string to a hooked nail and use that on the coin
box.

The Baths

Make sure the moodometer is at lying before you go in. Once inside,
you talk to the guy. Then stand by the big wheel and move the arrow
to scalding hot or freezing cold. Everyone will rush off and you
will be able to get the outfit you can see in the window.

The Town Arena

Click on the frog to move it aside. It is a good source of water,
if you need it - you can also get the odd eel simply by clicking at
its mouth. Note the footprints at the entrance.

City Limits

Pick up a couple of logs here.

Cow Shed

You need several flasks full of water. You combine the seeds with
the water and get a seedling. You put that in the hopper five
times in all, so that the arrow is pointing at the red number.
Watch what happens. Puncture the milk container with a straight
nail to get some cream with a flask. You can also speed up the
process by combining the seeds with an eel and adding water; in this
case, you only need to fill the hopper twice - but then, you need to
go fishing for eels.

Town Center

There are several locations here, and I'll tackle them one by one.

The Toy Factory

Open the padlock with a straight nail. Once inside, go through the
other door to Malcolm's pad. Here, look in the drawers and get the
nut-and-string and the staff under the bed. Don't be too hasty in
combining the nut with a bent nail to get the fishing tackle - read
on. Oh, and you can look through the family album, if you like.

Go out to the factory and click on the large book. You will see the
shadow of a toy. Put a log in the funnel of the machine and press
the green button. You get a toy soldier. Now manipulate the two
antennae-like appendages on the machine and click on the book
again. A different shadow of a toy will appear. If it is that of a
ball, put the shoe in the funnel and press the green button. You
get a ball. Go through the routine again with the antennae and
book; you can get a toy horse by putting a log in the funnel and
pressing the green key. You should end up with three toys.

The Cellar

Go down the hole into the cellar. Fill all your flasks with water.
(Later on, when you have a disguise, you can stand on the carpet by
clicking on one of the apples drawn on it, then clicking on the
other - see under Darm's.)

Note the bricked wall. When you are given the right information (on
the other hand, why wait?), you can combine sesame seeds with an eel
to get fertilized seeds (you can fish for eels in the sewer), put
them amongst the bricks, fill a flask with water and use that on the
seeds. This busts the bricks and you can go in. If you click on
the shell and use an empty flask on it you get a portal potion which
you can use in the Arena. This is a great shortcut which takes you
to the Isle of the Cats straight away, although you miss out on the
fun of the longer solution to this particular problem. Since you
can only use the portal potion once, leave the shell alone if you
don't want it; but you get extra points for busting the hole open.

From the cellar you can go up the stairs to the Town Hall, more
further on.

Darm's

You arrive here on the magic carpet from the cellar and leave the
same way. If you were to attempt a visit without a disguise, you'll
be recognized and you'll leave quite promptly. Once you get the
disguise, you can visit Darm and he will ask for a fishcream
sandwich. Give it to him and talk both to him and to the dragon.
You can use all your items on them to see if they give you any
useful info on them. Finally, use the staff on Darm repeatedly till
he leaves the room and then speak to the dragon - he will give you a
clue pointing to the bricked-up wall in the cellar.

Town Hall

You have to give the statue a sandwich in order to speak to it.
Once you've spoken, try your items on it and see if you can get any
clues.

The Fishcream Parlour

When you enter the place it's chock-a-block full of people and
Malcolm expresses the desire to make everyone go. To get stampede
points, get some seeds, the nut-and-string and go to the dump.
Place the seeds on the log on which the squirrel is standing (near
you) and use the nut on it to hypnotise it. Now you can pick it up
and go to the Parlour. Come to the front and put the squirrel on
the floor. Use the nut on the squirrel and watch. When everybody
is out and you leave, the parlour will be closed and bolted. If you
had trouble getting hold of sandwiches (and you need three), you
could always come armed with three (or whatever number) lots of
seeds, fish and cream and make the sandwiches when everyone leaves
and before you go out.

The Magician Lodge

You can only enter here if you are wearing the mime's outfit. Lie
when you talk to Zanthia. You can pull the alarm which will empty
the parlour - unfortunately, it is then also locked up.

The Strange Boy

He pops up all over, but he is mostly to be found in City Limits.
Be nice. You must offer him three toys and get try to get three
sandwiches in exchange. He will accept the toys at random, so
you'll have to try different ones on him. Sometimes he will take
two the same. I got lucky and had no trouble. At any rate, you
must get the sandwiches somehow. If he will not trade for all
three, then you have to get the Fishcream Parlour sorted.

The Crossroads

Use the scissors or broken glass to get a flower.

The Graveyard

Get another flower. Change to nice. Use the flowers on the grave
to speak to the ghost.

Pegasus Landing

Be nice. Talk to Zanthia and she will give you a clue.

The Dock

You can go to the point and use the string and hook contraption to
get eels. Later, and dressed up as the mime and carrying a
sandwich, you can talk to the dog and he will let you in the ship.
Try pricking him with something sharp, like a straight nail, to get
extra points.

So, there you have it. The main thing here, as you will have
gathered from all this, is either to get the portal potion or to get
the mime's outfit and to be left with one sandwich so that you can
get on the boat and sail to...
 

THE ISLE OF CATS

You will land in style. There is an altar here. If you were to go
left, you would see some statues. Be nice and talk both to the cat
and the dog. Don't attempt to wander into the jungle. Click on the
cart to get a lift.

The cart will take you to the three locations available, at random;
so that if you turn up at the Pirates, talk to them all but get back
on the cart.

In the Dog Fort you will find a machete, which is vital. Now
you can go into the jungle, but it is a very tiresome business,
since you have to hack the vegetation and kill any snakes you find
before you can proceed anywhere. The jungle wraps around on you, so
you might go around in circles forever. Which reminds me, jump into
puddles wherever you see them, otherwise you die eaten up by fleas.
If you forget and are at death's point, you can always get rid of
the fleas by clicking on the character and discarding them.

Right, to save a lot of wear and tear, from the Dog Fort go left,
left, left and up, collecting all the bones you find along the
way. Make sure you lie when you talk to Fluffy. Now go left, up
and up, again, collecting bones. (I found these directions varied
when I played the game again - so don't take me too seriously.)

Talk to the dog leaning on some rocks. Now, you can either give him
a bone, in which case he'll go off and bury it at random, or you can
place a bone where you want him to dig. Sometimes you get lucky and
get a gem. You must get six, so, when you run out of bones, go
right, clear the jungle, get more bones and go right again. Don't
forget to take the odd dip in the puddle. If you don't get any
bones, go right and this time try going left, clearing the jungle,
and then go up. Good luck to you.

Once you have the gems, go to Fluffy and show one to him. He will
give you a magic mouse. Go back to Dog Fort (from Fluffy, left,
up, up) and enter the ruins through the hole next to the dog. Go
right and use the mouse on each of the statues to see what each one
represents - make a note of it. Go out, change to nice and get on
the cart. You might go to the pirates (if you had not visited them
before, talk to them all) or to the altar; but you need to go to the
altar.

Use each gem on the altar to find out what they represent and make a
note of it. Go left and use the mouse on one of the balls. Now all
you have to do is to match the gems with the statues.

At the end you will get a crystal mouse. You will have to find your
own way to the pirates, since the cats are no longer pulling carts.
The directions in my case (it could be different in yours) were,
from the altar, right, left, left, up, right, left, righ, right.
Once you reach them, talk to the captain. When asked to perform
magic, use the mouse on the one-legged pirate. You are invited on
board and end up in Kyrandia, and from there you get sent to...
 

THE ENDS OF THE EARTH

This is a killer. Arm yourselves with patience and save your game.
You start with three coins. Buy insurance, the fins and the cleats
(press on the next button for that). Wear the cleats and you get a
shoehorn. Put it in the inventory. Press next the button for the
brolly and use the shoehorn on the machine. Remove the cleats by
clicking with the shoehorn on Malcolm.

Click twice on the first barrel to go down in it. Climb up using
the cleats (click up to the left of the screen). Swing across with
the brolly (click with it on the hook). Move to the extreme left
and use the brolly. Go into the cave. Again, move to the left and
use the brolly. Go into the cave. Remove the brolly by using the
cover on Malcolm. Put the fins on (click them on Malcolm) and use
the bungee string to get across (click it on the nearest hoop).
From this ledge you can climb up with the cleats or swim up, then
climb again, swing across with the brolly and swim up. Go into the
cave. You might have reached your destination (it varies), but if
you haven't, as you come out you can do any old thing; you need to
die and end up at the top again.

This bit, as I said, might not be necessary - but just in case it
is, at the top, but the toy float and the brolly. Take the second
barrel. Wear the toy and inflate the flower fully. Still wearing
the toy, click on the flower to jump across. Enter the cave. You
will see that the pictures have changed. Out, jump with the toy.
Swing across with the brolly and jump down again to the next cave.
Whichever cave is the one that changes, you will find yourself in...
 

LIMBO

At the Fish Court, you find out you are a slave to the queen by
virtue of a collar you wear around your neck. You will be forced to
play Tic Tac Toe, now and at other inconvenient moments. Change to
lying and lose the game, which is tougher than winning it. Then
click on the queen and lie to her till she gives you leave to go.
(This you will have to do several times, so I won't repeat these
instructions). On this occasion, you will finish up outside.
Change to nice, go back in and talk to the merman in the background.

Out, pick up the key, exit top left, use the staff on the fish to
the left and when the perch turns to the side, swipe his apple. You
will probably be interrupted here, but I'll ignore the interruptions
(you know what to do) and press on. From the university, go left
and watch. Talk to the fish by the gate (nice). Pick up the fondue
set. Get in the water course and pull the lever. You should finish
up in the dump. You can pick up two objects each time you land here
before the old bat tells you to get down. Talk to him.

Lie and say you are the tax collector and you'll get two coins.
Although you'll find it convenient to keep one of each of the
objects you find, give anything extra to the bat: a worm will gain
you a coin (feel free to sell it), three objects the same, another
coin. The object of the exercise is to get at least six coins as
soon as possible. Talk to the bat in all three moods to get some
useful information. Go on as many rides in the chute as necessary
to collect sufficient coins.

As soon as you have the money, go to the cannon and give five coins
to the fish. You will be shot to hell, literally. Change to nice
and speak to the guy on the line. Speak to the woman (normal or
lying) at the table and you will be told how to hold a Royal
Seance. Now you'll be pulled back to play tic-tac-toe. As soon as
you are free, take another ride on the chute and you should get a
newspaper from the dump. So long as you have a coin and a
newspaper, that's all you need. Use both on Malcolm.

Change to normal and go to the queen. Speak to her and you will be
challenged to another game. As soon as there are seven "pieces" on
the board, drop the newspaper and use the coin on it. The ghost
comes and you are free. Leave and go to the cannon again. Still at
"normal", speak to the fish and he will let you go for another
coin.

In hell, change to nice and speak to the guy to get ahead of him in
the queue. Watch what happens. You should get through to the
underworld. Talk to people as they come, but soon you will be sent
to the Boondocks. Use the machine and you will find yourself...

BACK IN KYRANDIA

At this point you are requested to choose between your better half
and your worst half. It's up to you, but I chose the good guy. I
don't know if it makes any difference.

The first thing you must do is go to the Castle, where you'll get
nabbed and asked to produce the six jewels of the Isle of Cats.
Talk to everyone there.

Visit the dump, if you like, and see if you can pick up anything
useful - you will certainly need a nail, a log, a whole flask and,
later, a broken one.

Again, you can do a variety of things. Go to the old Baths and you
will see that it is now a Pawn Broker. He will sell you seeds for
the items he asks - if you don't have that particular item, leave
and enter once more, and try again. The easiest one is flasks,
since you can pick up an endless supply from the dump.

Go to Malcolm's pad and find the portrait under the bed. (This next
bit is not necessary at the moment, or maybe never. It certainly
didn't get me anywhere, but it's up to you.) Go to the cellar and
travel to Darm's. If you speak to the guys, the dragon asks for a
squirrel. I tried that and it didn't work for some reason. I think
the only reason they are there is to supply you the Portal Potion
and, once you have found it, there is no need to come back.

Go up the stairs and have a look around and talk to the statue. You
can try using the items you are carrying on it, to find out whether
they are any use. Go back to the cellar. You can leave by clicking
on the pipe hole to the right of the door.

At the factory, use the log to make a toy horse. Leave the factory
and peek through the window of the Magician's Lodge. Use a nail on
the door and go in. Use a nail on the lock to free the three
"mice". Go back to the cellar and up the stairs and you'll find the
magician at work. Talk to her and then put the horse in the
cauldron she is stirring. Wait till it goes brown and use an empty
flask on it. Leave through the door and then through the pipe.

Find your way to the Pegasus Landing and use the potion. You finish
up in the inlet in which you met the pirates. Pick up the machete
and go left, left, left, right (Old Dog Fort), left, left, left, up
(Fluffy), collecting bones as you go. You'll need ten so give him
what you have and, if you don't have enough, go left, left and up.
He will give you a cheese-making machine. Go right and you'll be at
the altar. Go left, use the cheese-making machine on Malcolm and
pick up the cheese. Use it on the mouse statue and pick up all the
gems. Go back to Fluffy and he will give you a can. Use it on
yourself for an experience in a lifetime.

Now you've hit town again, you ought to know the items you were
carrying are to be found at the landing. No matter, right now go to
the dump where you'll find your two most precious items - the
portrait and the collar. Pick them up or, if you have no room, just
the collar. Go into the castle and talk to pegleg. Give him a
jewel and JC will come down. Hand JC the collar and watch. Well,
that got rid of them. Go to the dump to pick up a broken flask and
whatever else is left there.

Back at the castle you will see the two mice at the gate. Make some
cheese and give it to Brandon. Watch.

Cut two flowers with the broken glass. Go to the grave and summon
the ghost. Go to the Fishcream Parlour and make some cheese to give
to the Fishjerk. Talk to him. Leave and visit the Pawn Broker with
your jewels and buy some goods for fun. Try buying the dagger and
picking it up and see what happens. Save beforehand, just in case.

Go back to the Parlour. In your absence, the Fishjerk will have
mended the machine. He will ask for the ingredients needed to get
the whole thing going (seeds, cream and eels). You know how to get
them, so go ahead. Once you've put them in the funnel, you get a
sandwich. Go out.

Visit the pirate ship at the dock and click around for some fun.

Go back to the Parlour and ask the Fishjerk to get everyone to the
Town Hall. No dice.

Now go to the Old Town Hall and to the statue. Click on it till it
asks you about the ingredients for the seance. Pick up the crumpled
portrait and click it on the magic cabinet to the left. You get to
see a brief preview. Click again on the statue and it will ask you
for the ingredients to get the Kyrandians together. Give him the
sandwich. He will congratulate you and decide to go over to the
Parlour. Make with the portrait and the cabinet again and simply
sit back and watch.