Numerical Distributions in Logic Games

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• 2 Likes

  Markmark Alum Member

  May 2020 976 karma

  When you say distributions do you mean 3-1-1 2-2-1 4-1? In grouping games this is essential, I don't find it helpful in most other games. If you have an in out game with limited in out spaces it's typically pretty easy to see "oh I need 4 in which means 2 out" or it'll just be in the rules. Grouping games it's essential, other games I don't think so in most cases
• 1 Like

  ahnendc-1 Member

  May 2020 642 karma

  @FrenchyFuqua - I always think its a valuable exercise to figure out the numerical distributions up front; I try to contemplate them as I'm reading the rules / after I've read the rules. If I do not have a sense of the distribution I find myself absolutely paralyzed during the questions because there is so much indeterminate on the game board.

  If you continue to full-proof the games then you will start to recognize the types of rules that trigger distribution type inferences. E.g. - A three group grouping game with six pieces where one group must have more rules pieces then another and each group must have at least one piece assigned to it; well automatically we know we don't have a 2-2-2; instead we can have only either a 4-1-1 or a 3-2-1. It can be challenging to figure out all of the possibilities but I try to think it out from the perspective of maximizing/minimizing a particular number within. In the example, I just gave I asked myself, let's maximize the number of groups with only '1' piece in it, well it's impossible to have 3 groups of '1' because that would leave 3 pieces unplayed... however we can have two groups of '1' which would mean the remaining group has '4'. Then going down the scale, I put 1 group of 1, meaning 5 more pieces needed to be played across 2 groups the only possible distribution for which would be a group of 3 and a group of 2.

  As @Markmark mentioned this is particularly important for grouping games but also really important for In-out Games with Sub-Categorizes.
• Frenchy555 Live Member

  May 2020 393 karma

  @ahnendc-1 So when you go about figuring out the distributions beforehand do you write them down anywhere specific? Also, are you attempting to anticipate every single distribution when you do or do you focus on keeping it concise?
• Frenchy555 Live Member

  May 2020 edited May 2020 393 karma

  To add more detail to that question, I'm more referring to the complex situations, for example "A company paves 13 driveways, Monday through Sunday. They pave at least 1 but no more than 4 each day". This is going to lead to 7 different combinations. Would you just jot down the median, 3-3-3-1-1-1-1 combination above your board? Or is that too vague?
• 2 Likes

  Jonathan Wang Yearly Sage ⭐

  May 2020 6869 karma

  To me, numerical distributions are like any other inference. With any rule or rule interaction, we look at them because we want to understand whether it's a significantly limiting factor on our game or not. If so, you can explore either splitting on it directly or at least exploring further how it interacts with other significant elements of your game. If it turns out not to limit you especially meaningfully, you can backburner it.

  In general, I will always explore a numerical distribution because when they are one of the primary limiting factors of a game, they tend to do a huge amount of work. But if I can tell that it's not going to bear much fruit, I won't continue on just because it's a numerical distribution. Always remember that these things are means to an end, not ends unto themselves.
• Frenchy555 Live Member

  May 2020 393 karma

  Perfect! Much appreciation for the contributions. I now have the wind of numerical distributions at my back.
• 1 Like

  ahnendc-1 Member

  May 2020 642 karma

  @FrenchyFuqua to answer your earlier question, the unsatisfying answer is that it just depends. Most games in which the game board is indeterminate, resolve neatly into 2-3 distributions.

  In the situation you described above, I mapped out 6 different distributions of 7 groups of 13 members (let me know which one I missed).

  1) 4-4-1-1-1-1-1
  2) 4-3-2-1-1-1-1
  3) 4-2-2-2-1-1-1
  4) 3-3-2-1-1-1-1
  5) 3-2-2-2-2-1-1
  6) 2-2-2-2-2-2-1

  My thoughts are as follows on how you would approach this on the LSAT: 1) it's probably unlikely that there would be this amount of moving components on an LSAT game. I've seen games with multiple 'groups' (a sequencing game with 7 slots but where items can stack) but not very many items could go into each. Either way, I don't think it will be this complicated, so in a sense don't worry about what to do when there are this many variables.

  My second thought is that if you are in a game and you figure deduce the distribution to be something similar to this in terms of complexity, I would bet money on that you a missing a key inference upfront that would significantly reduce the number of available worlds. Sometimes these inferences can come from very subtle rules but when you combine them they significantly reduce the amount of available worlds. To build upon the example above with 7 groups of 4 or more. Imagine a rule that says game pieces X and Y must be together in a group with no one else. Can you figure out which distribution(s) that rule eliminates?

  Answer: distribution number one. Can you see why? It is because there must be a group of 2 and in distribution option one, a group of two never occurs. Likewise, what if there was a rule that said, game pieces L and W cannot be with any other game pieces. Can you figure out which distribution(s) that rule eliminates?

  Answer: distributions number six. Can you see why? It is because there must be at least two groups of 1 to accommodate this rule and that never occurs in distribution number six.

  Last example, there is a rule which says whatever group Y is in must have more pieces than the group which Z is in and is also the largest group. Can you figure out which distribution(s) this rule eliminates?

  Answer: distribution number four. This is because the group Y is in has to have either 3 or 4 pieces (because per the earlier rule the group in which Z was in must have 2 pieces) and there can't be any groups that also have 3 (if that is the largest group in the distribution) or 4 (if that is the largest group in the distribution)

  In this scenario we would be left with only distributions #2, #3 and #5. In this case, I would write down the different distributions. Most likely, I would create three separate Game Boards for each of the distributions and see what I could figure out from there.

  SPOILER ALERT............(Practice Test Six, Section Four, Game One, would be really illuminating I think for you).

  Also there is a game with jeweler selecting jewels for six rings that would be SUPER valuable for you do full proof. Another one would be the infamous game with male and female snakes and lizards.
• 1 Like

  Frenchy555 Live Member

  May 2020 393 karma

  @ahnendc-1 It was 3-3-3-1-1-1-1 that you left out in case you're still wondering. I'm certain that I have a drastically improved outlook on these now. Game 1 on PT 6 is at the top of my list now and I will check out the others that you mentioned. Thanks!