Setup and Rule Diagrams

[bella243]

Could someone please post a full setup of the game? Thanks!

[Adam Tyson]

Someone else will need to draw the diagrams for us, bella243, because I'm not all that adept at doing so in this format, but I am happy to describe it for you. I would create two columns for my groups, labeled 1 and 2 at the bottom of each column (as discussed earlier in this thread, you can choose to do them as rows - it's just a style choice, not a right or wrong thing - but I like columns for my groups). Each column/group would have 4 blank slots above the number.

My variables would be listed in the upper left corner, out of the way, by their subgroups, as follows:

A: FGH
C: VWXYZ

I would then write an "A" next to the bottom pair of slots in my columns, to indicate that at least that one slot must have an adult in it (F, G, or H).

A: __ __

The conditional rules get diagrammed off to the side, like so:

F2 G2
V1 W2

And for the last rule, since it divides these two children such that one is in boat 1 and the other is in boat 2, I would just put those as dual options in each column (I used the top slot in each, but it doesn't matter which slot you use, just so long as it is not the one marked for an adult since these two are both children):

X/V V/X

Be sure to mark H and Y as random variables, perhaps with an asterisk under each on in the list of variables.

At that point, you have the entire setup and can proceed to the questions. There are no not-laws, no variables placed in either group with any certainty. You could perhaps do three templates, revolving around the placement of the adults - F and G in 2 with H in 1, F and G in 1 with H in 2, and F in 1 and G in 2 with H free to go in either group - but that's just an option and not a requirement here (and that last template would not be very helpful, so probably not worth the effort to create them).

Draw that out and see if it makes sense, and then use that to attack the questions. Expect to do a lot of drawing for local questions since there is so little certainty in the main diagram!

[js2493]

Y V/W
W/V G
F/H H/F
X/Z Z/X

___ ___
F ___
G/H H/G
X/Z Z/X

This is what my two diagrams for the problem looked like (formatting too hard).

In the first scenario, the first boat has X/Z, F/H, V/W, and Y and the second boat has Z/X, H/F, G, and W/V
Second scenario, first boat has X/Z, G/H, and F while the second boat has Z/X and H/G. V, Y, and W can fit into any of the 3 remaining spaces (1 in the first boat, 2 in the second boat).

Is there any reason why these two diagrams alone wouldn't work? It breezes through the questions quite easily but I'm not sure if just these 2 diagrams are sufficient in covering every possible scenario.

[Rachael Wilkenfeld]

I think I'd agree with both of those, JS.

For me, I thought about this as a numerical distribution game. One boat has 2 adults, 2 kids. The other has 1 adult, 3 kids.
You have this well represented.

Your first senario has the 2-2 boat as boat 2, and the 1-3 boat as boat 1. If boat 1 only has 1 adult, it has to be F/H, because G1 requires F1 (thus 2 adults). X or Z is another of the slots on boat 1. That leaves two open slots for two of V, W, and Y. V and W can't go together on boat 1, so that means that Y must be on boat 1, with one of V/W. Boat 2 then has the left overs. It has two adults, G and F or H. It has the other of X/Z, and the other of V/W.

Your second scenario flipped the 2-2 boat and the 1-3 boat. In this one, your 2-2 boat was boat 1. Here, if we need 2 adults on boat 1, we know F must be one of the two. Otherwise, we'd have F in boat 2. which would require G in 2, and we'd be back in the first scenario. So our two adults in boat 1 are F, and one of G/H. Z/X are one of the kids. The last slot in boat 1 would need to be V/Y/W. In boat 2, we'd have the last adult (H/G), the other of X/Z, and the other two from the V/W/Y block.

Since we have covered all the possible scenarios (either 2-2 in boat 1, and 1-3 in boat 2, or 1-3 in boat 1 and 2-2 in boat 2) we can be confident moving forward with these templates.

Great work!