Linear Setup Practice Drill #5

[lakasil]

On page 103 for the problem dealing with a Jazz band using the variables of F G H J Q R S , I worked out the problem and realized that " S" splits up the problem because its in the middle. Therefore Q and R are placed under slots 2 and 6 because they can't be by each other? another question is what are the complete definitions for " Consecutively " and not Consecutive " ? ( I feel like I know the meaning but I just want to make sure to be on the right track so I do't confuse myself.

[lakasil]

SECOND QUESTION: on page 115 I am not fully understanding the concept of the problem when it comes to finding out the distributions. Is there anyway someone can explain a little more about to me so I can try to figure out the problem myself without looking at the answer for help?? please and thanks.

[Adam Tyson]

Regarding the Jazz band question on page 103, the two blocks created in the rules of FG and HJ have to be on either side of S. That means one of them goes in either 1-2 or 2-3, and the other goes in either 5-6 or 6-7. In any event, the blocks will cover slots 2 and 6, and that is why neither Q nor R can go in either of those two spaces. Try a template, as we talked about previously - place those two blocks somewhere and see what the options are for Q and R. You'll find the additional inference that those two can never be consecutive.

Which brings me to the second part of that question - consecutive means immediately next to each other in an order. Spots 1 and 2 are consecutive, whereas spots 1 and 3 are not. It means one right after another with nothing in-between. In games where there are ties allowed (two librarians both work on Saturday is a rule that comes to mind from a game I have worked on recently with some students), the two that work Saturday are NOT consecutive, because they are not next to each other in an order, but tied. Be careful about that one! If the game were to say "one works Saturday morning and the other works Saturday afternoon", then those two would be consecutive, and the one on Saturday afternoon would NOT be consecutive with the one that works on Friday, because the Saturday morning variable would be between them.

Keep at it!

[Adam Tyson]

Regarding the numerical distribution discussed on Page 115, the general idea is that you have to start by giving each group or slot the minimum number of variables required by the rules. Once that is done, put all the extra, leftover variables in one place, all together. That creates the most extreme distribution. From there, try to make it less extreme by moving some of those extras to another slot.

If I tell you that you have to give 5 donuts to two coworkers, what's the most extreme thing you could do? Give all 5 to one of them and leave the other with nothing - a 5-1 distribution. Now, start to move some of those donuts over from the large group to the empty one - you could have a 4-1 or a 3-2 distribution.

What if I said you had to give each coworker at least one donut? Then the 5-0 would be disallowed, and you would start by giving them each 1 and then giving the three leftovers to one of them, creating the 4-1 distribution as your starting point, the most extreme option.

Play around with that idea and read through the explanations in those pages and see if they make more sense to you now. Then get me some donuts, please. Five of them. Thanks!

[lakasil]

Adam, Thanks for the response! I understand the meaning of consecutive now even more and for the distributions. I suppose you just have to follow the rules and play around with the distributions? Another question that I have today is regarding to page 156 & 159 in the LGB. I'm not understanding for question 1 how the answer would be B because I thought that G had to be in Slots 3 or 5 . I see that JQRF are correct and that H is a Random, but How can G be first if looking at the question doesn't the rules have to still apply?

[Nikki Siclunov]

Hi lakasil,

Thanks for your question. As discussed on page 158, if G is inspected on day 3, then Q is inspected on day 5 and R is inspected on day 6. Since R is inspected on day 6, F must be inspected on day 1. This inference leads to the further inference that only two possible scenarios exist when G is inspected on day 3: F-H-G-J-Q-R or F-J-G-H-Q-R.

We cannot conclude from this line of reasoning that G must be inspected on either day 3 or day 5. This is an unwarranted inference, likely based on a faulty understanding of the conditional rule. The rule only stipulates what must be true IF G is inspected on day 3. If the sufficient condition is not met, however, no conclusions can be drawn about the placement of any other variable. Technically, G can be inspected on any of the six days.

Hope this helps!

Thanks,