Advanced Linear Setup Practice Drill #5

[Marce]

This is regarding #5 on pg. 47 of the Logic Games workbook, HOW was it concluded on pg 170 (answers) that M, K, and F are located in those exact places ???

[Dave Killoran]

Hi Marce,

Those general shelf placements come directly from the second and third rules, which read:

• M and K are both on the same shelf.
  K is two shelves above F.

So, that puts F on the bottom shelf, and MK on the top shelf. From there, you can place each book in any of the three spaces. This occurs because each space on each shelf does not have a number, and so it does not matter which space each book is placed in. Because the biographies can't be on the same shelf, I reserved one space at the "end" of each shelf for a biography, then I just started working to the left. You could have done it reverse, or totally different—because there is no space numbering, it doesn't matter!

Please let me know if that helps. Thanks!

[Marce]

Hi Dave,

Thanks, yes that helped. Does the same rule apply for Logic Games in general that include variables that don't have fixed numbered slots?

[Jon Denning]

Hi marce,

Jumping in here in Dave's place to hopefully help out

The answer to your question is yes! The reason we can feel confident putting those books onto shelves is because we're simply dealing with the grouping of things on the shelves, and not their order or position. If the scenario also said something like "the books are arranged left to right by increasing page count," for instance, "or books are either in the center of a shelf or at its edge" then we would have to worry about both shelf number and position and we'd need to be more careful about where we placed things. But since it's just the total group on the shelf we care about we can feel more confident placing them in there! A group of A, B, and C is the same no matter there order: B, C, A, or A, C, B, etc.

And that's really one of the big differences between linearity (sequencing) and grouping: in linear situations order tends to matter, whereas in grouping it's generally composition that matters and not the order itself.

So in linear we might have five students sit in a row of desks one behind the next from the front of the classroom to the back. So order matters here, since we want to know each person's position relative to the other people and to the classroom itself (at the front, in the middle, second to last in the back, etc). But the group probably doesn't: it's the same five people, after all, just moving around desk to desk.

In grouping it might be five students are sitting in two rows of desks, with one row of two desks and another tow of three desks. Here we'd likely worry about who goes in which row, "X is in the row of 3," but not about which specific desk they'd get (their exact position) unless that was specified as well ("if Y is in the row of 3 Y must sit in the desk closest to the front").

I hope that helps!

[Marce]

thanks