Lesson Four: Logic Games and Logical Reasoning Flashcards
–LOGIC GAMES–
Linearity
Involves two basic variable sets:
- the base (numbered list of variables in a straight line).
- the variables ordered (put in order) by the base.
Explain the 2 aspects of linearity with the following example: “Seven singers are scheduled in seven singing positions.”
Seven singers: variables ordered by base.
Seven singing positions: base
Advanced Linear Games usually contain ____ to ____ variables sets.
3; 5
“Six runners -P, Q, R, S, T, U- compete in a marathon. Each runner finishes the race, and no 2 runners finish at the same time.”
Rules:
- Four of the runners are female and two are male.
- Each runner is either an amateur or a professional but not both.
Identify the variable sets in the game. (SEE NOTES for further examples)
Six runner positions (base) : 1 2 3 4 5 6
Six runners: PQRSTU
Male / Female: : ___ ___ ___ ___ ___ ___ FFFFMM
Amateur/Professional: : ___ ___ ___ ___ ___ ___
In cases where you have several horizontal variable set ups from top to bottom, this is called a _____________.
stack
Repeated Variable Sets:
Most games use their variables sets (however many) only once. However, test takers do include some games in which a variable set may be repeated.
Repeated Variable Sets (Example Problem): “Over a period of 6 weeks (BASE ALREADY) 6 restaurants - A, B, C, D, E, F - will be reviewed once (1-1 NUMERICAL GAME) by small news paper editor Gomez (VARIABLE SET), and once by the head writer Hughes (VARIABLE SET). Each reviewer reviews exactly one restaurant per week.
Write out the variable set for each
Gomez: ___ ___ ___ ___ ___ ___ ABCDEF
Hughes:___ ___ ___ ___ ___ ___ ABCDEF
Weeks: 1, 2, 3, 4, 5, 6
Disadvantage of Repeated Variable Sets:
The disadvantage of repeated variable sets is that the same variables are repeated twice, and you have to be able to differentiate between the variables used in one variable set and another.
What is the best way to differentiate between similar variables on different variable sets?
Using subscripts.
“Hughes will review restaurant B before Gomez reviews E.”
B(h)━━━E(g)
“Hughes will review restaurant B before Gomez reviews B.”
B(h)━━━B(g)
Linked Variable Set Rules
With linked variable set rules, we are able to link/connect variables from one variable set up to another.
Linked Variable Set rules work as much as they do in practice (when you’re actively placing ___________ in the slots on separate variable ________) as in _________________. It’s important you use __________ and _____________ rules whenever you’re diagramming for multiple stacks (variable sets).
variables; sets; diagramming; block; sequencing
Let’s review this problem again:
“Six runners -P, Q, R, S, T, U- compete in a marathon. Each runner finishes the race, and no 2 runners finish at the same time.”
Rules:
- Four of the runners are female and two are male.
- Each runner is either an amateur or a professional but not both.
Now let’s add a new rule: “The two male runners are professionals.”
Diagram the rules of the game using block rules.
This new rule connects two variable sets. We know there are exactly two males, and we know both are each professionals. So we need exactly two blocks.
┍━─┓
┃ M ┃
┃ P ┃
┗━─┛
┍━─┓
┃ M ┃
┃ P ┃
┗━─┛
Blocks with Horizontal and Vertical Aspects (Linked Variable Set Rules)
Test takers want to challenge students to using blocks to diagram not just horizontal or just vertical, but both.
Example: “The car with a blue exterior is assembled immediately before the car with the red interior, but immediately after the car with a manual transmission.”
Draw out the block rules
Identify and draw out your variable setups.
Variable Setups
- Based on the rules, we know the Manual Transmission comes first, the blue exterior second, and the red interior third.”
Trans. : __ __ __ __ __ __
Int. : __ __ __ __ __ __
Ext. : __ __ __ __ __ __
Cars: 1 2 3 4 5 6
Block Rules:
- Many test takers would be tempted to set up their block rule as follows:
┍━━━━━━━━─┓
┃ M(t)━B(e)━R(i) ┃
┗━━━━━━━━─┛
While technically this does incapsulate what the games rules suggest, this is not a completely full-proof block rule.
It doesn’t account for the Verticality of the stack in our game.
Instead Diagram like this:
┍━━━━━─┓
T ┃ M __ __ ┃
I ┃ __ __ R ┃
E ┃ __ B __ ┃
┗━━━━━─┛
This model of the block rule DOES account for the verticality of the game. (BTW, if you’re wondering why there’s only 3 spots in the block rule, it’s because there are only 3 steps in the rule regarding Manual transmission, the blue exterior, and red interior.)
