The Seven Cities of Maple

[Lepton]

Here they are

This is another mathgrant classic, in case you were wondering. [img]/Forums/smile.gif[/img]

[Foggy]

It looked familiar, but I can't remember if there's a hook to it.

Answer invizzed
[Going from left to right, top to bottom, towns are Function, Calcularia, Distributive, Geometra, Binomia, Equats, and Algebra. The signs are for Calcularia, Geometra, Function, Algebra, Distributive, Binomia and Equats.]

I'll post a fuller solution latter.

------------------
Before we tally up your prizes, let's see if your husband is conscious yet -- David Leisure on MwC

[raphael_as]

I have the positions of F and E exchanged - Unless the sign which says "fix sign" is actually wrong (Im not sure if thats part of the game) there is (I think!) no town in your solution which can be 2 from E whilst also being 4 from A.

[Foggy]

I believe that's the point of the "fix sign" note.

Full solution:
[I'll refer to the circles as 1, 2, etc. going from left to right, top to bottom. I'll refer to the signs as I, II, III, going from left to right, top to bottom.

According to sign III, Algebra is 6 miles away. This means that sign III must be #1 or #7, as must Algebra. The cities 3 miles away from either #1 or #7 are #4 or #5, so Geometria is one of these two towns.

Two signs (I and VI) are 4 miles away from Geometria. If Geometria were #5, there is no way two different signs could be 4 miles away from Geometria. Geometria is therefore #4, and the two signs I and VI are #2 and #5 in some order.

According to sign IV, Calcularia is 5 away from sign IV. This means these must be #1 and #6 or #2 and #7 in some order. Calcularia is also 2 miles away from either #2 or #5, which means Calcularia can't be #1 or #7. it's #2 or #6. If it's #6, then sign VII can only be #2, which is impossible. So Calcularia is #2, and sign IV is #7. Sign III is therefore #1, and Algebra is #7. Sign VI can't be #2, it's #5; Sign I is therefore #2.

Binomia is 3 miles away from #7. #4 is already Geometria, so Binomia #5. Binomia is 4 miles away from sign II. Sign II must therefore be #4. Distributive is 1 mile away from #4, and is therefore #3.

Sign VII is either #4 or #6; it's no longer possible for it be #4, so it's #6. Sign V must be in #3, the only city remaining. Something on sign V is incorrect. Yet Algebra (#7) is 4 miles away, so Equats must be wrong. The only two unnamed cities are #1 and #6. Equats can't be number #1, so Equats is #6, and Function is #1.]



------------------
Before we tally up your prizes, let's see if your husband is conscious yet -- David Leisure on MwC

[Lambert]

The towns are as follows:

.	E	C
D	.	.
G	.	B
.	F	.
.	A	.

and the signs are in these towns respectively (reading left to right, top to bottom)

C, G;
E, A, D;
B, F.

[dave10000]

[Rutabega Boy]

There really isn't any way someone can know for sure that the "fix sign" pertains to the numbers. The assumption the author hopes the solver will make is that the "fix sign" clue is relevant and critical to the solution. However, by the same token, we should consider "river sticks" and "hire dept" to be relevant and critical, too. So I think the fault lies with the phrasing of the puzzle. As such, I think either of the two unique solutions posted thus far are correct. Still, it's a good puzzle, I'd say. A jolly good one, if you ask me.

[mathgrant]

The sign is crooked. That's why it needs to be fixed. The distances are right.

People were confused over that the first time I posted it, too. That's why I tried to tell Lepton to use less artsy signs. . .

[S A P]

I agree with raphael_as and Lambert. I solved by [ creating a grid that maps the distance relationships between the cities, with the top city being t, the next being u, and so forth. By inspection, Algebra must be t or z, but t isn't 4 from anything, so Algebra is z. Geometra has distances 4, 3, and 4, and only w has those values. Calcularia, with distances 5, 2, and 4, is either u or y. Because of Calcularia's relationship to Geometria (the sixth sign), the only option for Calcularia is u. The only city 4 from Algebra is v, which forces Equats to be t. Inspection quickly gives the last couple cities. ]



[This message has been edited by S A P (edited 06-19-2004 09:53 AM).]

[Foggy]

Given what mathgrant said, then Equats and Function change places in my solution above.

But it is pretty frustrating. There's a lot of excess "stuff" in the puzzle, mostly artwork in the signs. But why the "fix sign" note? It's not really humorous, so it seems like it's supposed to be a part of the solution. Being observant should never be a bad thing in a puzzle.

[mikeamok]

it is humorous! i think so, anyway. at first glance, it appears the ground is sloped and the sign is standing straight up. but the sign is actually broken and leaning to the side. so the photographer had to have tilted the camera to get the sign to look straight. at least, that's how i interpreted it, and straight away.

i miss the original story that went along with the puzzle, though. the Journey CD kind of doesn't make sense now.

by the way, the link in Lepton's post is wrong. the first p should be uppercase, and the second should be lowercase.

[jims]

It would have at least been a little interesting if the 5th sign had a real error on it.

The solution, assuming no errors, is top-bottom, left-right:
{ E, C, D, G, B, F, A }

If the sign had an error, it had to be the line with { "Equats 2" }
Which changes the answer to:
{ F, C, D, G, B, E, A }

[This message has been edited by jims (edited 06-18-2004 09:54 AM).]

[Rigelian1]

I have a solution to the puzzle. Lambert's map was correct, but my sign placement is a little different. I Labeled the pictures numberically from left to right, top to bottom as they appear in the puzzle (i.e. 1 is the sign which says Geometra 4, Distributive 3. 2 is Distributive 1, Binomia 4 etc). So with that being said: E is 3, C is 1, D is 5, G is 2, B is 6, F is 7, and A is 4.

[dARKhORN]

I agree with Lambert

[jmm]

I'm stuck. Sign 3 must be located middle top or middle bottom. Either way G is middle left or middle right. Sign 1 says D and G are 1 mile apart. That means G is middle left with D 1 mile above. Sign 6 says C is 2 miles from G. That makes C 1 mile above middle bottom. Sign 7 is 4 miles from C. That makes 7 upper right. Sign 6 must be 2 miles from C and 4 miles from G. That makes it middle right. BUT... sign 1 must be upper right or middle right to be 3 miles from D and 4 miles from G.

[Foggy]

jmm, Sign 1 only says that D and G are 3 and 4 miles away from that sign; it implies no relation between D and G themselves. As an example, the number 10 is 3 away from 7, and 4 away from 14.

------------------
Before we tally up your prizes, let's see if your husband is conscious yet -- David Leisure on MwC

[Speeder]

My last post must have disappeared in the changeover but never mind...

I just wanted to say I got the same result as Lambert.

Speeder.

[Guest]