- PowerScore Staff
- Posts: 907
- Joined: Apr 11, 2011
- Wed Dec 05, 2018 12:00 am
#62046
What follows is my take on the third game from November 2018, referred to by most as "the mining game" and widely reported to be the hardest on the test.
Before I outline how to approach this particular setup, however, let me take a moment to make a broader point about handling inevitable moments of unfamiliarity and confusion on the LSAT.
I see this game as a reflection of a central/key LSAT truth, and one that anyone prepping for a future exam would do well to keep in mind: this test, no matter how difficult it appears at times, can always be beaten if you maintain your composure, formulate a strategy of attack (or at least a reasonable means of making some sort of headway), and keep soldiering on. And then the solution required often turns out to be much, much easier than one might expect! This game rewarded those who stayed calm and simply kept some momentum going, whether by an informed analysis of the questions and what they have to teach—doing 13, 16, and 17 first, for example, makes 14 and 15 far easier—or merely toying with possibilities, as we'll soon see...not an ideal approach in most instances—aimlessly playing with hypotheticals is a serious waste of time in more conventional LG situations—but it's always better than the more popular alternative: freaking out and doing nothing.
So let this be a lesson to you. When, not if but when, you encounter moments of confusion or challenge on the LSAT, whether as a novel game or a dense RC passage or a convoluted LR stimulus, always remember that if you keep your cool and continue some forward motion you can get through it. And likely with far less of a struggle than you might at first expect
Now, to the game!
While a Basic Linear game by standard classification, the nature of the scenario and rules left a lot of people struggling to make sense of what was occurring and how to begin their setup. The result? People panicked and froze, staring at the page but ultimately making no headway. As mentioned above, that reaction must be avoided at all costs!
So what can we do inch our way forward when the path ahead is unclear? The answer in this case—and many others—is to begin sketching hypotheticals of how the game can play out, and in the process gain a better understanding of the underlying mechanics and various inferences that are hard to see at first glance.
What we find as a result of this approach is somewhat remarkable here: this game, tough as it seems, has only four total solutions. Four. And two of those occur as part of a single template, meaning just three lines of hypotheticals show you every single outcome possible from the very start. I'll list those three "templates" below (quotes to indicate they're really more full solutions than typical templates), but please take a moment right now to consider the larger lesson: when the way forward is wholly unclear, there's often tremendous reward for those willing to just start working!
Now here are those four solutions, with a few notes on how I arrived at them (what drove my thinking in creating these):
First, there are a couple of inferences/ideas worth understanding in this game that I think will help the solutions to come make more sense. (1) The three H variables (headquarters) are precious, because they're so critical when placing the other pieces: the most you can ever get of G or K is two in a row and then you must use an H, and any switch from G to K or vice versa can't be consecutive, but requires an H separator; (2) because there has to be an H between any G/K set, you can immediately place an H in September (between the G in August and K in October; putting either a G or K in Sept would have Gs and Ks touching, with is forbidden); (3) that also means putting an H at either end of the series, in March or November, is wasteful because that H isn't being used to separate...you can try this with an H in March, for instance, and immediately see trouble: with two Hs used at that point (March and the required September from point #2 above) you have a stretch of four empty months from April to July with only a single H to place, and no matter how you try from this point you're going to violate a rule (three in a row, G and K touching, or the need for more than three of some letter). So you want Hs to come between other letters rather than at the very beginning or very end of them all.
The math of the three points just mentioned amounts to this: the most distance between any two Hs is two spots. Go three spots between Hs and you have either three in a row of G or K, or G and K adjacent. Neither is allowed.
NOTE THIS THOUGH: even if you failed to catch most of that and simply started trying different arrangements, you'd either learn much of what I just wrote in the process, or find that so few arrangements work that the game is solved despite not truly grasping all of its details/inferences. Again, forward progress is the key!
So imagine we start, totally at random, with a G in the first position (I'll just choose alphabetically). That's two of our Gs used.
G __ __ __ __ G H K __
Where can we put our third to avoid Ks and have enough Hs for our transitions? Well, one option is to put the final G in month two, April, and start with a GG block!
G G __ __ __ G H K __
That MUST be followed by an H, and since we're out of Gs and don't want Hs back to back (again, wasteful when we need them as buffers), we'd follow that with a K. It looks like this so far:
G G H K __ G H K __ (put another way, we follow GG with an H because we must, and with no Gs remaining
the empty spot in front of G in August must be an H, leaving only Ks for the empties: G G H __ H G H K __ )
We have an H and a K left, and it's clear where they go! To avoid a KG sequence we'll use an H in July, and our last K down at the end in November:
G G H K H G H K K (solution #1)
Voila! One down.
Of course, that was only one possibility for our final G if we have a G starting things off; we also could've placed it down in July preceding our August G from rule 3:
G __ __ __ G G H K __
With only Hs and Ks remaining, consider where we'd place them to abide by the known restrictions...we'd have to put an H after that first G, and right before the GG block (otherwise Ks would touch those Gs, and that's bad):
G H __ H G G H K __
With only two Ks to go, they slot into the final two open spots:
G H K H G G H K K (solution #2)
And that's it if we start with a G!
I explained above why starting with an H won't work—try it if you haven't and you'll discover the problem(s)—so let's now begin with a K and see how that looks:
K __ __ __ __ G H K __
We're down to our last K at this point, so let's try what we did with G and pair it with one of the Ks already there. I'll try a KK block in the first two months and see what happens:
K K __ __ __ G H K __
With no more Ks we have to start using Hs, with one following the KK block up front, and one at the very end:
K K H __ __ G H K H
So far so good...but wait. We only have two Gs left, and placing them is going to make a three-G (GGG) block! That's not allowed, so our KK start here won't work.
Let's instead place our final K at the very end and see how that plays out:
K __ __ __ __ G H K K
We're down to Hs and Gs, and we know K and G can't touch, which forces an H into month 2:
K H __ __ __ G H K K
Again, if we do an HH block right now we'd get three Gs in a row, so we need a G in the third position:
K H G __ __ G H K K
Finally, we have an H and a G to go, and they can fill either spot, leaving us with this as our two final solutions (in one):
K H G H/G G/H G H K K (solutions #3 and #4)
And that's all she wrote!
You can see immediately that you've answered questions 14 (K is always in November in every setup above) and 15 (H in September, an idea we had from the start but that would be clearly evident at some point along this journey otherwise). Then 16 and 17 just require tracking along the appropriate template(s), and 13 was a simple case of four rules violations.
So don't be disheartened if you struggled with this game! Nearly everyone did. Instead take as much comfort as you can in the fact that the LSAT is, cover to cover, beatable if you keep your wits about you and never stop fighting.
I hope this helps
Before I outline how to approach this particular setup, however, let me take a moment to make a broader point about handling inevitable moments of unfamiliarity and confusion on the LSAT.
I see this game as a reflection of a central/key LSAT truth, and one that anyone prepping for a future exam would do well to keep in mind: this test, no matter how difficult it appears at times, can always be beaten if you maintain your composure, formulate a strategy of attack (or at least a reasonable means of making some sort of headway), and keep soldiering on. And then the solution required often turns out to be much, much easier than one might expect! This game rewarded those who stayed calm and simply kept some momentum going, whether by an informed analysis of the questions and what they have to teach—doing 13, 16, and 17 first, for example, makes 14 and 15 far easier—or merely toying with possibilities, as we'll soon see...not an ideal approach in most instances—aimlessly playing with hypotheticals is a serious waste of time in more conventional LG situations—but it's always better than the more popular alternative: freaking out and doing nothing.
So let this be a lesson to you. When, not if but when, you encounter moments of confusion or challenge on the LSAT, whether as a novel game or a dense RC passage or a convoluted LR stimulus, always remember that if you keep your cool and continue some forward motion you can get through it. And likely with far less of a struggle than you might at first expect
Now, to the game!
While a Basic Linear game by standard classification, the nature of the scenario and rules left a lot of people struggling to make sense of what was occurring and how to begin their setup. The result? People panicked and froze, staring at the page but ultimately making no headway. As mentioned above, that reaction must be avoided at all costs!
So what can we do inch our way forward when the path ahead is unclear? The answer in this case—and many others—is to begin sketching hypotheticals of how the game can play out, and in the process gain a better understanding of the underlying mechanics and various inferences that are hard to see at first glance.
What we find as a result of this approach is somewhat remarkable here: this game, tough as it seems, has only four total solutions. Four. And two of those occur as part of a single template, meaning just three lines of hypotheticals show you every single outcome possible from the very start. I'll list those three "templates" below (quotes to indicate they're really more full solutions than typical templates), but please take a moment right now to consider the larger lesson: when the way forward is wholly unclear, there's often tremendous reward for those willing to just start working!
Now here are those four solutions, with a few notes on how I arrived at them (what drove my thinking in creating these):
First, there are a couple of inferences/ideas worth understanding in this game that I think will help the solutions to come make more sense. (1) The three H variables (headquarters) are precious, because they're so critical when placing the other pieces: the most you can ever get of G or K is two in a row and then you must use an H, and any switch from G to K or vice versa can't be consecutive, but requires an H separator; (2) because there has to be an H between any G/K set, you can immediately place an H in September (between the G in August and K in October; putting either a G or K in Sept would have Gs and Ks touching, with is forbidden); (3) that also means putting an H at either end of the series, in March or November, is wasteful because that H isn't being used to separate...you can try this with an H in March, for instance, and immediately see trouble: with two Hs used at that point (March and the required September from point #2 above) you have a stretch of four empty months from April to July with only a single H to place, and no matter how you try from this point you're going to violate a rule (three in a row, G and K touching, or the need for more than three of some letter). So you want Hs to come between other letters rather than at the very beginning or very end of them all.
The math of the three points just mentioned amounts to this: the most distance between any two Hs is two spots. Go three spots between Hs and you have either three in a row of G or K, or G and K adjacent. Neither is allowed.
NOTE THIS THOUGH: even if you failed to catch most of that and simply started trying different arrangements, you'd either learn much of what I just wrote in the process, or find that so few arrangements work that the game is solved despite not truly grasping all of its details/inferences. Again, forward progress is the key!
So imagine we start, totally at random, with a G in the first position (I'll just choose alphabetically). That's two of our Gs used.
G __ __ __ __ G H K __Where can we put our third to avoid Ks and have enough Hs for our transitions? Well, one option is to put the final G in month two, April, and start with a GG block!
G G __ __ __ G H K __That MUST be followed by an H, and since we're out of Gs and don't want Hs back to back (again, wasteful when we need them as buffers), we'd follow that with a K. It looks like this so far:
G G H K __ G H K __ (put another way, we follow GG with an H because we must, and with no Gs remaining the empty spot in front of G in August must be an H, leaving only Ks for the empties: G G H __ H G H K __ )We have an H and a K left, and it's clear where they go! To avoid a KG sequence we'll use an H in July, and our last K down at the end in November:
G G H K H G H K K (solution #1)Voila! One down.
Of course, that was only one possibility for our final G if we have a G starting things off; we also could've placed it down in July preceding our August G from rule 3:
G __ __ __ G G H K __With only Hs and Ks remaining, consider where we'd place them to abide by the known restrictions...we'd have to put an H after that first G, and right before the GG block (otherwise Ks would touch those Gs, and that's bad):
G H __ H G G H K __With only two Ks to go, they slot into the final two open spots:
G H K H G G H K K (solution #2)And that's it if we start with a G!
I explained above why starting with an H won't work—try it if you haven't and you'll discover the problem(s)—so let's now begin with a K and see how that looks:
K __ __ __ __ G H K __We're down to our last K at this point, so let's try what we did with G and pair it with one of the Ks already there. I'll try a KK block in the first two months and see what happens:
K K __ __ __ G H K __With no more Ks we have to start using Hs, with one following the KK block up front, and one at the very end:
K K H __ __ G H K HSo far so good...but wait. We only have two Gs left, and placing them is going to make a three-G (GGG) block! That's not allowed, so our KK start here won't work.
Let's instead place our final K at the very end and see how that plays out:
K __ __ __ __ G H K KWe're down to Hs and Gs, and we know K and G can't touch, which forces an H into month 2:
K H __ __ __ G H K KAgain, if we do an HH block right now we'd get three Gs in a row, so we need a G in the third position:
K H G __ __ G H K KFinally, we have an H and a G to go, and they can fill either spot, leaving us with this as our two final solutions (in one):
K H G H/G G/H G H K K (solutions #3 and #4)And that's all she wrote!
You can see immediately that you've answered questions 14 (K is always in November in every setup above) and 15 (H in September, an idea we had from the start but that would be clearly evident at some point along this journey otherwise). Then 16 and 17 just require tracking along the appropriate template(s), and 13 was a simple case of four rules violations.
So don't be disheartened if you struggled with this game! Nearly everyone did. Instead take as much comfort as you can in the fact that the LSAT is, cover to cover, beatable if you keep your wits about you and never stop fighting.
I hope this helps
Jon Denning
PowerScore Test Preparation
Follow me on Twitter at https://twitter.com/jonmdenning
My LSAT Articles: http://blog.powerscore.com/lsat/author/jon-denning
PowerScore Test Preparation
Follow me on Twitter at https://twitter.com/jonmdenning
My LSAT Articles: http://blog.powerscore.com/lsat/author/jon-denning