Free AI Website BuilderAxelcris G. Suladay
Mergel Ann G. Millendez
Trisha B. Vista
Klotski is a special type of sliding puzzle first emerged in the early 20th
century. It refers to a variety of sliding block or tile games with the goal of
moving a specific block to a predetermined spot. This investigation aimed to
determine the minimum number of moves by altering the game’s regulation
that requires a player to move a specific tile or block from one corner of the
puzzle to its opposite corner. The results of the investigation proposed the
use of the formula M = 8s − 11 in determining the minimum number of
moves (M) of a square-shaped Klotski given the number of columns/rows
(s) of the puzzle. Alternatively, the formula M = 6l + 2w − 13 was also
proposed to determine the minimum number of moves (L) of a rectangular shaped
Klotski with l and w as the number of columns and rows, and
l > w. In the case where only the product (P) and difference (d) of the
dimensions are given, the formula MPd = 4√d2 + 4P +2d−13 may be used
to determine the minimum number of moves (MPd). It is recommended
that further studies must be conducted to determine the other possible real
life application of the concept and additional investigations must be done
for other cases of the puzzle.
Keywords: Arithmetic, Klotski, Minimum Number of Moves, Pattern, Sliding
Puzzle
Klotski is a type of a sliding puzzle that have started and gained popularity in
the early 20th century. It refers to a whole group of similar sliding-block puzzles
with a same objective of moving a certain block to a predetermined location.[3]
Within the frame, the blocks can be moved anywhere by sliding—not turning,
lifting or jumping. To complete the sliding puzzle, the starting and finishing
positions are typically provided.
Upon watching a player do the Klotski puzzle by moving a tile from one place
to another, the investigators observed some patterns that are related and was
tackled in their Mathematics class in the previous school year. This urges them
to perform a short experimentation of moving a tile in a diagonal direction in
order to find the minimum number of moves and to formulate a mathematical
investigation about the Klotski puzzle in hopes of discovering concepts that may
contribute in the study of mathematics.
Thus, this study focuses on exploring the Klotski puzzle and to generate formulas
out of the number of moves it needed to complete the puzzle. This investigation
also aims to determine the minimum possible number of moves in solving a square
or rectangular-shaped Klotski with the aid of the different mathematical concepts,
particularly the arithmetic sequence.
Like other varieties of sliding puzzle, Klotski is also known as a challenging
game that brings entertainment to people in all ages. This game also enhance an
individual’s problem solving skills, critical thinking skills and other mathematical
related skills. Moreover, this game might not just be a ”simple game” for it has
the potential to unfold mathematical concepts that have a significant contribution
to mathematical research.
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