Types / Finite Slots

Average Questions Per Test1.2
Predicted Questions on Modern Test6.7
Finite slot rules are common limiting factors present in assignment and grouping games, where the rules revolve around placing actors in categories or grouping them together. Examples include games based on selecting actors for a committee, grouping children to parent chaperones, or assigning colors to stained-glass windows.

A finite slots rule simply limits the number of potential slots for a given selection or group; however, unlike finite rules for sequencing, these rules are less rare and fluid slots are more common. Because fluid slots make the game more modular and increase the possibilities the examinee must consider, finite slot games are typically easier both to diagram and apply for questions.

Because finite slot rules are so fundamental, we're not going to spend a lot of time diagramming them or covering them. The Sample Questions with Explanations has two games with introductory paragraphs that describe finite rules, as well as a couple of rules that require you to limit the game further by filling in those slots with actors.

While reading this first paragraph, try to parse the language in the sentences that tells you
  1. exactly how many actors you have to choose from, 
  2. how many slots are available, 
  3. how many times you can or must choose each actor, and 
  4. how many actors that thus leaves over.
This information is incredibly important for solving any assignment or grouping game, and leads you directly to understanding the min and max part of the Zen of 180 system.


Which key words and phrases let you know this is a finite slots game?

There are eight total actors, and each one can either be reduced or not (we can't reduce one actor more than once). However, we only have exactly five slots we have to fill, at both the minimum and maximum.This language is clearer than most assignment games, so hopefully it's easy for you to see that we'll have three actors left over in every possible permutation.

After reading through the rest of the rules to make sure that nothing changes the structure of the game, you should draw a simple workbench that represents the five reduced slots, emphasizes the min/max, number of non-reduced (i.e., non-assigned) actors. Unlike in a sequencing game, the slots don't need to be numbered because an actor is either in/out, and their relative position is irrelevant.

The workbench with all of the actors is on the left. The right is the start of Zen of 180's MMFR analysis.

The second game paragraph has a very similar structure, but has two rules below the paragraph that further limit the finite slots. I've gone ahead and highlighted the relevant portions of the paragraph text that combine to mean that the game has finite slots. Can you spot which two rules will allow us to start filling in actors to those finite slots?

Note that the key phrase "from ... will be selected" indicates an assignment game.

The basic workbench for this game is very similar to the previous game. In fact, the min/max analysis is also very similar. Can you explain why? If you need help, go back up to the numbered instructions and then check your answer below the image.

With seven total actors but only 4 slots for the dinner, three people will be left out.

However, there's more to this game that makes it even easier! There are two rules that allow us to draw actors into our finite slots, and thus we also classify them as finite slot rules. The first step is to read the rules below the base paragraph--they're set off by a tab--and ask yourself, "Can I draw something into my diagram that will always be true?" Read the rules above and see if you can find two examples before looking below.

If you picked the first two rules, you're headed in the right direction!

Alright. So we know that we have to have J or K, as well as N or P. Those pairs apparently don't play well with each other, but are too important to leave out altogether. But we don't know which ones to draw into our diagram, do we? And what slot would we draw them into, anyway?

Well, the second issue is easy to deal away with: the slots are functionally identical, and thus it really doesn't matter where we draw in our deductions. Unlike a sequencing game, each slot in this simple assignment game means exactly the same thing: that actor gets to go to dinner.

The first question requires us to understand conditional separate rules, but a simple maxim of the Zen of 180 diagramming system will make your life easier: as soon as you know there are only two possibilities, draw them in. Like so:


Notice that J/K effectively takes up a seat, as does N/P.

The two finite slot rules combine to mean that half of our game is halfway done: we know that those two slots have to have JP, JN, KN, or KP. Rather than write all of those possibilities out, it's far better to have a single diagram with the possibilities intact but simply drawn.

The J/K means that either J or K could take up that slot, but that no other actor can be assigned to that "slot." Note, again, it doesn't matter that it's the "first" slot; there is no first slot in a strict assignment game. Instead, think of it as a reservation that you can draw in so you don't forget to save a seat for one of those two.

The circle around the J/K and N/P remind us that those actors are "trapped" inside those slots, and that we can't draw them in any other slot. They're either assigned that slot, or they don't get to go to the dinner at all This comes from the "but ... both cannot be selected" language: if we assign J in our diagram, we can't then put K in an open slot on the right.  This is technically a conditional separate rule, but I just wanted to clarify in case you had a burning desire to understand--you'll find a more complete intro on that rule's own page.
GroupTestQ #SectionAnswerYour AnswerDistractorDifficulty
June 2007 6-10 (1/6)June 200761CMedium
June 2007 6-10 (1/6)June 200771AMedium
June 2007 6-10 (1/6)June 200781DAHard
June 2007 6-10 (1/6)June 200791EBHard
June 2007 6-10 (1/6)June 2007101DB/EHard
PT 64 13-18 (2/6)PT 64132CEasy
PT 64 13-18 (2/6)PT 64142EMedium
PT 64 13-18 (2/6)PT 64152DCMedium
PT 64 13-18 (2/6)PT 64162CAHard
PT 64 13-18 (2/6)PT 64172BAHard
PT 64 13-18 (2/6)PT 64182DA/CHard
PT 64 19-23 (1/8)PT 64192BMedium
PT 64 19-23 (1/8)PT 64202ADHard
PT 64 19-23 (1/8)PT 64212ACMedium
PT 64 19-23 (1/8)PT 64222DMedium
PT 64 19-23 (1/8)PT 64232CMedium
PT 63 1-5 (2/10)PT 6312EEasy
PT 63 1-5 (2/10)PT 6322BEasy
PT 63 1-5 (2/10)PT 6332AVery Easy
PT 63 1-5 (2/10)PT 6342CEasy
PT 63 1-5 (2/10)PT 6352ED/BVery Hard
PT 62 14-18 (1/8)PT 62143CAHard
PT 62 14-18 (1/8)PT 62153ADHard
PT 62 14-18 (1/8)PT 62163AEHard
PT 62 14-18 (1/8)PT 62173DAHard
PT 62 14-18 (1/8)PT 62183EA/DVery Hard
PT 61 12-17 (1/9)PT 61123DEasy
PT 61 12-17 (1/9)PT 61133DMedium
PT 61 12-17 (1/9)PT 61143BEasy
PT 61 12-17 (1/9)PT 61153AMedium
PT 61 12-17 (1/9)PT 61163EAHard
PT 61 12-17 (1/9)PT 61173BA/DVery Hard
PT 60 13-17 (1/9)PT 60132EEasy
PT 60 13-17 (1/9)PT 60142DMedium
PT 60 13-17 (1/9)PT 60152EVery Easy
PT 60 13-17 (1/9)PT 60162AEasy
PT 60 13-17 (1/9)PT 60172BDMedium
PT 60 18-23 (1/9)PT 60182AVery Easy
PT 60 18-23 (1/9)PT 60192BC/DHard
PT 60 18-23 (1/9)PT 60202BCMedium
PT 60 18-23 (1/9)PT 60212DAMedium
PT 60 18-23 (1/9)PT 60222EEasy
PT 60 18-23 (1/9)PT 60232CMedium
PT 59 11-16 (3/9)PT 59111DMedium
PT 59 11-16 (3/9)PT 59121EMedium
PT 59 11-16 (3/9)PT 59131CAHard
PT 59 11-16 (3/9)PT 59141AHard
PT 59 11-16 (3/9)PT 59151DMedium
PT 59 11-16 (3/9)PT 59161ACHard
PT 58 13-17 (1/9)PT 58133DVery Easy
PT 58 13-17 (1/9)PT 58143DMedium
PT 58 13-17 (1/9)PT 58153BEasy
PT 58 13-17 (1/9)PT 58163BVery Easy
PT 58 13-17 (1/9)PT 58173CAMedium
PT 57 12-17 (2/9)PT 57121BEasy
PT 57 12-17 (2/9)PT 57131DBMedium
PT 57 12-17 (2/9)PT 57141ACMedium
PT 57 12-17 (2/9)PT 57151ECHard
PT 57 12-17 (2/9)PT 57161ADHard
PT 57 12-17 (2/9)PT 57171BCMedium
PT 56 12-16 (1/5)PT 56121DEasy
PT 56 12-16 (1/5)PT 56131CHard
PT 56 12-16 (1/5)PT 56141AHard
PT 56 12-16 (1/5)PT 56151AMedium
PT 56 12-16 (1/5)PT 56161EMedium
PT 56 17-23 (1/7)PT 56171AEasy
PT 56 17-23 (1/7)PT 56181AMedium
PT 56 17-23 (1/7)PT 56191CDHard
PT 56 17-23 (1/7)PT 56201DBHard
PT 56 17-23 (1/7)PT 56211EBHard
PT 56 17-23 (1/7)PT 56221EMedium
PT 56 17-23 (1/7)PT 56231BEMedium
PT 55 1-6 (1/6)PT 5514DVery Easy
PT 55 1-6 (1/6)PT 5524CEasy
PT 55 1-6 (1/6)PT 5534AEasy
PT 55 1-6 (1/6)PT 5544BMedium
PT 55 1-6 (1/6)PT 5554EEasy
PT 55 1-6 (1/6)PT 5564CEasy
PT 55 19-23 (1/8)PT 55194EEasy
PT 55 19-23 (1/8)PT 55204DMedium
PT 55 19-23 (1/8)PT 55214DMedium
PT 55 19-23 (1/8)PT 55224CBHard
PT 55 19-23 (1/8)PT 55234DBHard
PT 53 18-23 (1/8)PT 53182EEasy
PT 53 18-23 (1/8)PT 53192AMedium
PT 53 18-23 (1/8)PT 53202BMedium
PT 53 18-23 (1/8)PT 53212CMedium
PT 53 18-23 (1/8)PT 53222EDHard
PT 53 18-23 (1/8)PT 53232BEasy
PT 51 1-5 (2/8)PT 5114DEasy
PT 51 1-5 (2/8)PT 5124AMedium
PT 51 1-5 (2/8)PT 5134EMedium
PT 51 1-5 (2/8)PT 5144CEasy
PT 51 1-5 (2/8)PT 5154EMedium
PT 51 11-15 (1/11)PT 51114DEasy
PT 51 11-15 (1/11)PT 51124EMedium
PT 51 11-15 (1/11)PT 51134DEasy
PT 51 11-15 (1/11)PT 51144DMedium
PT 51 11-15 (1/11)PT 51154EDHard
PT 50 6-11 (1/11)PT 5063EEasy
PT 50 6-11 (1/11)PT 5073DEasy
PT 50 6-11 (1/11)PT 5083BEasy
PT 50 6-11 (1/11)PT 5093AVery Easy
PT 50 6-11 (1/11)PT 50103EMedium
PT 50 6-11 (1/11)PT 50113BEHard
PT 49 13-17 (1/6)PT 49131AVery Easy
PT 49 13-17 (1/6)PT 49141CMedium
PT 49 13-17 (1/6)PT 49151AEasy
PT 49 13-17 (1/6)PT 49161DEasy
PT 49 13-17 (1/6)PT 49171EMedium
PT 48 13-17 (2/10)PT 48132CDHard
PT 48 13-17 (2/10)PT 48142AEasy
PT 48 13-17 (2/10)PT 48152DMedium
PT 48 13-17 (2/10)PT 48162CBMedium
PT 48 13-17 (2/10)PT 48172CBHard
PT 46 7-11 (3/7)PT 4674BEasy
PT 46 7-11 (3/7)PT 4684CEasy
PT 46 7-11 (3/7)PT 4694BMedium
PT 46 7-11 (3/7)PT 46104CMedium
PT 46 7-11 (3/7)PT 46114BMedium
PT 46 17-22 (1/9)PT 46174CEasy
PT 46 17-22 (1/9)PT 46184CMedium
PT 46 17-22 (1/9)PT 46194BMedium
PT 46 17-22 (1/9)PT 46204DMedium
PT 46 17-22 (1/9)PT 46214EEasy
PT 46 17-22 (1/9)PT 46224DMedium
PT 46 12-16 (1/7)PT 46124AVery Easy
PT 46 12-16 (1/7)PT 46134CMedium
PT 46 12-16 (1/7)PT 46144EMedium
PT 46 12-16 (1/7)PT 46154DEasy
PT 46 12-16 (1/7)PT 46164BEasy
PT 45 18-22 (1/7)PT 45183AVery Easy
PT 45 18-22 (1/7)PT 45193AEasy
PT 45 18-22 (1/7)PT 45203EEasy
PT 45 18-22 (1/7)PT 45213CVery Easy
PT 45 18-22 (1/7)PT 45223CEasy
PT 45 7-12 (2/9)PT 4573AEasy
PT 45 7-12 (2/9)PT 4583AVery Easy
PT 45 7-12 (2/9)PT 4593AVery Easy
PT 45 7-12 (2/9)PT 45103AVery Easy
PT 45 7-12 (2/9)PT 45113CEasy
PT 45 7-12 (2/9)PT 45123EEasy
PT 44 13-17 (1/8)PT 44133EMedium
PT 44 13-17 (1/8)PT 44143CMedium
PT 44 13-17 (1/8)PT 44153AEasy
PT 44 13-17 (1/8)PT 44163EDMedium
PT 44 13-17 (1/8)PT 44173DCHard
PT 44 18-22 (1/10)PT 44183AEasy
PT 44 18-22 (1/10)PT 44193EVery Easy
PT 44 18-22 (1/10)PT 44203EMedium
PT 44 18-22 (1/10)PT 44213DMedium
PT 44 18-22 (1/10)PT 44223CEasy
PT 43 13-17 (2/9)PT 43134BMedium
PT 43 13-17 (2/9)PT 43144BMedium
PT 43 13-17 (2/9)PT 43154DEasy
PT 43 13-17 (2/9)PT 43164BDMedium
PT 43 13-17 (2/9)PT 43174BVery Easy
PT 43 18-22 (3/9)PT 43184DCMedium
PT 43 18-22 (3/9)PT 43194CVery Easy
PT 43 18-22 (3/9)PT 43204EVery Easy
PT 43 18-22 (3/9)PT 43214AEasy
PT 43 18-22 (3/9)PT 43224CDMedium
PT 40 18-23 (1/11)PT 40182DVery Easy
PT 40 18-23 (1/11)PT 40192CEasy
PT 40 18-23 (1/11)PT 40202CVery Easy
PT 40 18-23 (1/11)PT 40212BEasy
PT 40 18-23 (1/11)PT 40222AEasy
PT 40 18-23 (1/11)PT 40232BEasy
PT 39 6-11 (3/8)PT 3961DEasy
PT 39 6-11 (3/8)PT 3971EVery Easy
PT 39 6-11 (3/8)PT 3981CEasy
PT 39 6-11 (3/8)PT 3991BVery Easy
PT 39 6-11 (3/8)PT 39101AEMedium
PT 39 6-11 (3/8)PT 39111AEasy
PT 38 14-19 (2/7)PT 38142EVery Easy
PT 38 14-19 (2/7)PT 38152DEasy
PT 38 14-19 (2/7)PT 38162CHard
PT 38 14-19 (2/7)PT 38172BEasy
PT 38 14-19 (2/7)PT 38182BEasy
PT 38 14-19 (2/7)PT 38192CVery Easy
PT 37 1-5 (2/9)PT 3713DEasy
PT 37 1-5 (2/9)PT 3723BVery Easy
PT 37 1-5 (2/9)PT 3733DVery Easy
PT 37 1-5 (2/9)PT 3743DEasy
PT 37 1-5 (2/9)PT 3753DMedium
PT 37 12-18 (2/8)PT 37123BVery Easy
PT 37 12-18 (2/8)PT 37133AMedium
PT 37 12-18 (2/8)PT 37143DEasy
PT 37 12-18 (2/8)PT 37153EEasy
PT 37 12-18 (2/8)PT 37163EMedium
PT 37 12-18 (2/8)PT 37173CEasy
PT 37 12-18 (2/8)PT 37183EDHard
PT 36 7-13 (1/8)PT 3674EVery Easy
PT 36 7-13 (1/8)PT 3684AEasy
PT 36 7-13 (1/8)PT 3694CEasy
PT 36 7-13 (1/8)PT 36104CMedium
PT 36 7-13 (1/8)PT 36114AEasy
PT 36 7-13 (1/8)PT 36124ABMedium
PT 36 7-13 (1/8)PT 36134BEasy
PT 36 14-18 (1/13)PT 36144EHard
PT 36 14-18 (1/13)PT 36154ADHard
PT 36 14-18 (1/13)PT 36164DBHard
PT 36 14-18 (1/13)PT 36174BDHard
PT 36 14-18 (1/13)PT 36184CBHard
PT 35 1-5 (2/8)PT 3513DEasy
PT 35 1-5 (2/8)PT 3523AVery Easy
PT 35 1-5 (2/8)PT 3533DVery Easy
PT 35 1-5 (2/8)PT 3543BVery Easy
PT 35 1-5 (2/8)PT 3553AMedium
PT 35 13-17 (1/11)PT 35133AVery Easy
PT 35 13-17 (1/11)PT 35143BEasy
PT 35 13-17 (1/11)PT 35153CVery Easy
PT 35 13-17 (1/11)PT 35163EEasy
PT 35 13-17 (1/11)PT 35173EEasy
PT 34 1-7 (2/11)PT 3414CVery Easy
PT 34 1-7 (2/11)PT 3424EAHard
PT 34 1-7 (2/11)PT 3434BMedium
PT 34 1-7 (2/11)PT 3444DMedium
PT 34 1-7 (2/11)PT 3454AMedium
PT 34 1-7 (2/11)PT 3464ECHard
PT 34 1-7 (2/11)PT 3474BMedium
PT 34 8-12 (2/8)PT 3484EMedium
PT 34 8-12 (2/8)PT 3494AMedium
PT 34 8-12 (2/8)PT 34104CAHard
PT 34 8-12 (2/8)PT 34114DEasy
PT 34 8-12 (2/8)PT 34124BDMedium
PT 33 13-18 (1/9)PT 33134DVery Easy
PT 33 13-18 (1/9)PT 33144EDMedium
PT 33 13-18 (1/9)PT 33154EEasy
PT 33 13-18 (1/9)PT 33164DVery Easy
PT 33 13-18 (1/9)PT 33174DVery Easy
PT 33 13-18 (1/9)PT 33184BEasy
PT 33 19-23 (3/13)PT 33194BEasy
PT 33 19-23 (3/13)PT 33204DVery Easy
PT 33 19-23 (3/13)PT 33214BEasy
PT 33 19-23 (3/13)PT 33224EEasy
PT 33 19-23 (3/13)PT 33234DVery Easy
PT 32 19-24 (2/10)PT 32193EEasy
PT 32 19-24 (2/10)PT 32203BEasy
PT 32 19-24 (2/10)PT 32213DEasy
PT 32 19-24 (2/10)PT 32223BMedium
PT 32 19-24 (2/10)PT 32233AMedium
PT 32 19-24 (2/10)PT 32243DEasy
PT 31 14-18 (1/8)PT 31141CEasy
PT 31 14-18 (1/8)PT 31151BEasy
PT 31 14-18 (1/8)PT 31161AVery Easy
PT 31 14-18 (1/8)PT 31171EMedium
PT 31 14-18 (1/8)PT 31181AMedium
PT 31 1-6 (1/11)PT 3111EEasy
PT 31 1-6 (1/11)PT 3121BEasy
PT 31 1-6 (1/11)PT 3131DEasy
PT 31 1-6 (1/11)PT 3141CMedium
PT 31 1-6 (1/11)PT 3151AVery Easy
PT 31 1-6 (1/11)PT 3161CEasy
PT 30 11-16 (2/12)PT 30111BEasy
PT 30 11-16 (2/12)PT 30121AEasy
PT 30 11-16 (2/12)PT 30131BEasy
PT 30 11-16 (2/12)PT 30141EEasy
PT 30 11-16 (2/12)PT 30151BMedium
PT 30 11-16 (2/12)PT 30161AB/DHard
PT 30 1-5 (1/8)PT 3011DVery Easy
PT 30 1-5 (1/8)PT 3021AEasy
PT 30 1-5 (1/8)PT 3031CMedium
PT 30 1-5 (1/8)PT 3041DEasy
PT 30 1-5 (1/8)PT 3051BEasy
PT 29 1-6 (1/6)PT 2913DVery Easy
PT 29 1-6 (1/6)PT 2923CMedium
PT 29 1-6 (1/6)PT 2933AEasy
PT 29 1-6 (1/6)PT 2943BVery Easy
PT 29 1-6 (1/6)PT 2953BVery Easy
PT 29 1-6 (1/6)PT 2963CEasy
PT 29 7-13 (2/7)PT 2973DMedium
PT 29 7-13 (2/7)PT 2983EEasy
PT 29 7-13 (2/7)PT 2993EDHard
PT 29 7-13 (2/7)PT 29103EMedium
PT 29 7-13 (2/7)PT 29113BMedium
PT 29 7-13 (2/7)PT 29123BMedium
PT 29 7-13 (2/7)PT 29133CHard
PT 29 20-24 (2/13)PT 29203EEasy
PT 29 20-24 (2/13)PT 29213AEasy
PT 29 20-24 (2/13)PT 29223BEMedium
PT 29 20-24 (2/13)PT 29233DMedium
PT 29 20-24 (2/13)PT 29243EBMedium
PT 28 19-23 (3/9)PT 28192DEasy
PT 28 19-23 (3/9)PT 28202EVery Easy
PT 28 19-23 (3/9)PT 28212AVery Easy
PT 28 19-23 (3/9)PT 28222CVery Easy
PT 28 19-23 (3/9)PT 28232EVery Easy
PT 27 13-19 (1/10)PT 27132DEasy
PT 27 13-19 (1/10)PT 27142AVery Easy
PT 27 13-19 (1/10)PT 27152CEVery Hard
PT 27 13-19 (1/10)PT 27162AMedium
PT 27 13-19 (1/10)PT 27172EHard
PT 27 13-19 (1/10)PT 27182BMedium
PT 27 13-19 (1/10)PT 27192EVery Easy
PT 26 1-7 (2/10)PT 2611CVery Easy
PT 26 1-7 (2/10)PT 2621BVery Easy
PT 26 1-7 (2/10)PT 2631AVery Easy
PT 26 1-7 (2/10)PT 2641DVery Easy
PT 26 1-7 (2/10)PT 2651EVery Easy
PT 26 1-7 (2/10)PT 2661AMedium
PT 26 1-7 (2/10)PT 2671DVery Easy
PT 26 19-24 (2/10)PT 26191BVery Easy
PT 26 19-24 (2/10)PT 26201DEasy
PT 26 19-24 (2/10)PT 26211ADMedium
PT 26 19-24 (2/10)PT 26221ABHard
PT 26 19-24 (2/10)PT 26231ADHard
PT 26 19-24 (2/10)PT 26241EEasy
PT 26 13-18 (1/9)PT 26131DEasy
PT 26 13-18 (1/9)PT 26141DEasy
PT 26 13-18 (1/9)PT 26151BVery Easy
PT 26 13-18 (1/9)PT 26161BCMedium
PT 26 13-18 (1/9)PT 26171EEasy
PT 26 13-18 (1/9)PT 26181CMedium
PT 25 1-5 (2/10)PT 2513BVery Easy
PT 25 1-5 (2/10)PT 2523BEasy
PT 25 1-5 (2/10)PT 2533DVery Easy
PT 25 1-5 (2/10)PT 2543EEasy
PT 25 1-5 (2/10)PT 2553DMedium
PT 25 6-12 (1/12)PT 2563CEasy
PT 25 6-12 (1/12)PT 2573AMedium
PT 25 6-12 (1/12)PT 2583BEasy
PT 25 6-12 (1/12)PT 2593EVery Easy
PT 25 6-12 (1/12)PT 25103BEasy
PT 25 6-12 (1/12)PT 25113EVery Easy
PT 25 6-12 (1/12)PT 25123EEasy
PT 25 13-18 (2/16)PT 25133CEasy
PT 25 13-18 (2/16)PT 25143ABVery Hard
PT 25 13-18 (2/16)PT 25153DVery Easy
PT 25 13-18 (2/16)PT 25163CEasy
PT 25 13-18 (2/16)PT 25173BAHard
PT 25 13-18 (2/16)PT 25183CMedium
PT 24 18-23 (2/10)PT 24184EEasy
PT 24 18-23 (2/10)PT 24194EEasy
PT 24 18-23 (2/10)PT 24204EEasy
PT 24 18-23 (2/10)PT 24214EEasy
PT 24 18-23 (2/10)PT 24224DEasy
PT 24 18-23 (2/10)PT 24234CMedium
PT 68 6-10 (1/12)PT 6864DCHard
PT 68 6-10 (1/12)PT 6874EDHard
PT 68 6-10 (1/12)PT 6884CDHard
PT 68 6-10 (1/12)PT 6894BCHard
PT 68 6-10 (1/12)PT 68104DCHard