Gameplay - Fundamentals of Game Design - page 265

Logic and Mathematical Challenges
Logical and mathematical reasoning has been part of gameplay since the dawn of
human history. Logic provides the basis for strategic thinking in any turn-based
game of perfect information and many other games in which the player can make
precise deductions from reliable data. This section is confined to logic puzzles .The
“Strategy” section, later in the chapter, deals with strategic thinking.
Mathematics underlies all games in which chance plays a role or the player does
not have reliable data and so must reason from probabilities. Such games present
explicit mathematical challenges to the player: If he doesn't compute the odds
when playing poker, or at least know the odds and reason correctly given what he
knows, he's much more likely to lose.
In the broadest sense, any game that includes numeric relationships offers a mathe-
matical challenge, because the player must learn how those relationships work.
Much of the time, games present mathematical challenges implicitly, couching
numeric relationships in other terms: physics, strategy, or economics. (For an
example about strategy, see the section “Production Rates, Unit Numbers, and
Lanchester's Laws” in Chapter 14, “Strategy Games.”) Other sections of this chapter
deal with implicit mathematical challenges.
FORMAL LOGIC PUZZLES
A puzzle is a mental challenge with at least one specific solution. Formal logic means
classic deductive logic in which the definition of the puzzle contains, or explains,
everything the player needs to know to solve the puzzle. A formal logic puzzle can
be solved by reasoning power alone. It shouldn't require any outside knowledge.
Many other types of puzzles require logic too, but they also expect the player to
supply some additional information.
A logic puzzle typically presents the player with a collection of objects related in
ways that are consistent but not directly obvious. To solve the puzzle, the player
must put the objects into a specified configuration. The player manipulates the
objects and receives feedback about their relationships, which he eventually comes
to understand by observation and deduction. Rubik's Cube, a classic logic puzzle
with a simple mechanism, consists of so many cubes that move in ways so intri-
cately interrelated that it is quite difficult to solve.
Adventure games often present logic puzzles as combination locks or other machin-
ery that the player must learn to manipulate because those devices make sense in
the fantasy world in which the game exists. Other puzzle-based games don't try to
be realistic but concentrate on offering an interesting variety of challenges.
To adjust the diffic ult y of a logic challenge, raise or lower the number of objects to
be manipulated and the number of possible ways in which the player can manipu-
late them. A Rubik's Cube with four tiles per side (a 2 ✕ 2 ✕ 2 cube) instead of nine
(3 ✕ 3 ✕ 3) would be far easier to solve.