Numerical Distribution

[ja93]

Hello PowerScore,

I'm new to this forum, so first off I'd like to thank you guys and let you know how helpful the bibles been to me thus far.

I am, however, a bit confused with Numerical Distribution. On page 327 it says: "Numerical Distribution follows this rule: the numbers add up to an amount equal to the total number of variables in the set being allocated; the number of separate numbers is equal the number of elements receiving the allocated set. So how come on the page 338 (the explanation for June 2005 Question-the subcommittee game) it says the distribution is 3-2-1-1-1, which is a total of six numbers if the receiving set is the 9 spaces of the subcommittee. Based on this distribution it seems as if the spaces are the allocated set (9) and the committee members are the receiving set (6), as there are six total numbers and the numbers add to nine. This, however, confuses me because in the game we are allocating the committee members to the subcommittees, so why is the distribution implying the opposite? Aren't the committee members being allocated (selected) to subcommittees?

Furthermore, on page 337, in the 2-2-2-1-1 distribution, the apartments are the allocated set and the floors are the receiving set. This makes sense to me because the apartments are being allocated to the floors (a total of five numbers and the numbers equal to 8), but it seems to contradict the june 2005 explanation, as the subcommittees are being allocated to the committee members. It seems backwards to me.


I guess the whole "allocate" and "receiver" aspect is confusing me.

Looking forward to hearing from you.
Thank you in advance!

[David Boyle]

Dear ja93,

Thanks for your questions. Glad the "bibles" were helpful!

The June 2005 game is somewhat "unpleasant" in that there are committee members AND subcommittees AND spaces to juggle. Also confusing is that each member can serve on several subcommittees, and thus in several spaces. So, while you are basically allocating members to committees, you could also say that committee spaces are being allocated to the members. (Imagine a boss saying, "I'm assigining, or allocating, these three tasks to you to do." He could also have said, "I'm allocating you into these three tasks.")

The apartment-to-floor allocation on p. 327 (not p. 337) does make sense, since you can't have an apartment that's on more than one floor! The horrible thing about the June 2005 game is that a subcommittee can have three members--and also, a member can be on more than one subcommittee. Ugh.

Anyway: in a sense, the nomenclature of "allocate" or "receiver" is not all-important as long as you know how to solve the problem. Allocating subcommittee spaces to each committee member in the June 2005 game is a convenient way to think about things, even though you are also allocating the members to the spaces. Things have multiple aspects at times...(just as light can be viewed as either particles or waves, the quantum physicists might tell us).

Hope that was helpful. Please let us know if you have any other questions. Have a great day!

[ja93]

Hi David,

Thank you for your quick response!

It definitely clears some things up but also raises the question of how do you know which set is allocating and which set is receiving, as allocating people to tasks seems less intuitive to me than allocating tasks to people. Likewise allocating spaces to members seems less "natural" than allocating members to into the spaces. So is there any trick or method to know which set is the receiving and which is the allocating in Numerical Distribution?

Looking forward to hearing from you. Thanks for your help thus far!

[ja93]

Just to add--I guess what also confuses me is that I thought that the base would always be the "receiving set" because it receives the variables, but in the June 2005 subcommittee problem the base was the allocated set for the Numerical Distribution. The same holds true for the example (the advertisement one), that I just posted and explained in my first post.

Thanks again.

[Adam Tyson]

Hi ja,

I'll add my two cents here. I agree with David, don't get too hung up on the terminology of allocate and receive. Rather, focus on the fact that there is a numerical relationship, and then look for where the variability is - that is, what can change, compared to what cannot.

In the Subcommittee game, what is fixed is the number of subcommittees (3) and the number of spaces per subcommittee (also 3), giving us 9 fixed, determined, absolutely known spaces. They aren't moving, changing, or going anywhere. The members, however, are moving around, some on just one committee and some on multiple, so that's where you focus your efforts on determining the distribution.

Think of it this way - even though there are only 6 members, FGHIMP, at least one of them is a three-peat. Think of the each repetition as being a new variable - If it was F, for example, that was on all three, your distribution might start with FFFGHIMP (and you would notice that you only have 8 now to fill the 9 spaces, so you know that one, and only one, of the others must repeat once - perhaps FFFGGHIMP). That might help you to better understand the numerical distribution of 3-2-1-1-1-1.

[ja93]

Thank you, that does clear things up a little.


What also confuses me is that in some distributions a digit higher than 1, 2 for instance, means two different variables fill that slot (the "apartment" example mentioned in previous posts) and in other distributions it means a variable is allocated twice (the "subcommittee" example). I guess every problem has to be approached different and the digits representing the numerical distribution (even if the same) depict different things depending on the problem. Is this correct?

Also I have one more question regarding numerical distribution and balance. Is numerical distribution used to balance an overfunded or underfunded game?

I understand the basics of underfunded and overfunded but an example in the book confused me, so now I'm not sure if I fully understand it. How is the problem on page 343, "the seven film buffs" game on the Dec 1998 Lsat, a balanced game as stated by the book if its 7 buffs into 3 films. Isn't this an overfunded game?

On page 353, the "tour" game of the June 2005 Lsat, is underfunded according to the book because its 3 divisions into 5 tours. That makes sense. But how come this game is considered underfunded (3 into 5) and the film buff game is balanced if its 7 into 3 which to me seems overfunded.

Looking forward to hearing from you!

Thanks again for your help. Much appreciated.

[Nikki Siclunov]

Let me add my 2c.

I guess every problem has to be approached different and the digits representing the numerical distribution (even if the same) depict different things depending on the problem. Is this correct?

Absolutely. The digits representing the numerical distribution usually refer to the number of spaces available in each group (if it's a grouping game). With underfunded games, however, the digits might be referring to how many times each variable can be allocated. It all depends on the context of the game.

Is numerical distribution used to balance an overfunded or underfunded game?

It could be used to determine the numerical relationships in any type of game, including over/under-funded games. It is not used to balance anything; Balance is a reflection of the relationship between the number of variables in a game and the total number of spaces available for those variables.

How is the problem on page 343, "the seven film buffs" game on the Dec 1998 Lsat, a balanced game as stated by the book if its 7 buffs into 3 films. Isn't this an overfunded game?

The game is Balanced-Moving, thanks to the Numerical Distribution analysis resulting from the first rule. Within each of the two distributions (1-2-4 and 2-4-1), the game is perfectly balanced, since there aren't any "left-over" variables once each film buff is allocated to one of the three films. It's also "Moving" because the balanced distribution of variables to spaces shifts between two different distributions. This game would be "overloaded" if, for instance, each film had to be seen by exactly two film buffs. Then you'd have an extra film buff, which is the hallmark of an overloaded game.

Does that make sense? Let me know!

[ja93]

Thank you Nikki that was very helpful and clears things up!

[ja93]

But just one more thing--can't the "tour" game be considered balanced if some tours are repeated twice which evens out its distribution to the five days? (its three tours for five days but some are repeated twice, so its a total of five tours for five days, which would seem to be balanced)?

[Nikki Siclunov]

The short answer to your question is, yes. Underfunded games are typically made Balanced by either using a single variable multiple times, or by having specific (reserved) empty spaces. This is covered in the Logic Games Bible

Glad I could help!