Diagram

[jaf51200]

I was wondering what kind of game of grouping game Manhattan would characterize this as? It looks like an open grouping game. Is the optimal setup to make the three parks as the base of the game board and then place five slots under each of the parks for the five different types of attractions?

[MarkK142]

Very confused by this game...would appreciate a diagram and a strategy for taking this game on. Thanks

[ohthatpatrick]

We'd call this Open Grouping.

There's a special subtype of Open Grouping that many of teachers refer to as "Options" games, and it's the only time when you end up making the MORE NUMEROUS thing the base of your diagram.

Options games mainly happened in PT40-50.
- there's one where every car at least one of Sunroof / Leather / Power steering
- there's one where every record store has at least one of Folk / Opera / Rock / Jazz
- there's one where every student reviews at least one of Sunset / Tamerlane / Undulation

This game almost looks like that, but not quite. I would still set it up like a normal grouping game in which the 3 parks are the base of the diagram.

In Grouping games, we're usually asking ourselves these main questions:
- How many things / how many groups?
- Do they tell us how many things in each group (closed) or is it up for grabs (open)?
- Does each thing go exactly once (normal/easier) or is it up for grabs (rare/harder)

We know our three groups, J / I / H, each have at least one thing.
We do NOT have any min/max given for our five things, f / g/ m / p / t (until we hit the rules)

Since there is a rule that nothing has both P and F, we know that no group would ever have all 5 things. It looks like the max any group could have would be 4. And we learn that group I has exactly one thing. And we learn that J can't have T, so it would have a max of 3.

It's hard to draw an open board in this typing environment, so I'll just rotate it sideways:

Jes: [ __ ] __ __
Isl: [ __ ]
Hil: [ __ ] __ __ __

From the rules, we know that
G = 2
Jes: M, ~T
P --> ~F
T --> G
M --> P

There are exactly two G's, so that means there cannot be three T's (or else that would trigger three G's). But we don't have to have two T's. It's fine for G to be somewhere even if T isn't there.

Whenever we have multiple conditionals, we ask ourselves if they can chain together. In this case, we know
M --> P --> ~F

Whenever we have conditionals, we ask ourselves if we can apply them to any particular facts.

We know that Jes has M, so we know that Jes has P and can't have F.
We know that Isl has only 1, so it can't have M or T, which trigger additional things to be in.

Updating our board ...
Jes: M, P, __ ....... ~T, ~F
Isl: [ __ ] .... ~M, ~T
Hil: [ __ ] __ __ __

updating our roster
F G M P T
...2

It looks like that's about where we'd stop.

BIG PAUSE
Jes definitely has M and P. It might have a third, which would only be G.
Isl has only one, and it must be G, P, or F.
Hil could have anywhere from 1 - 4. For this one, we still need to keep in mind the two conditionals and the 2 G rule.