QiYi Kiotski 4x4 (magnetic 4×4 sliding puzzle) is a classic “15-puzzle” in a modern design: a 4×4 grid, 15 numbered tiles and one empty space that allows you to slide the tiles and arrange the numbers in order from 1 to 15.

Puzzle features

• Magnetic construction. Magnets are built into the base and/or tiles, so the pieces are held firmly to the frame. The tiles do not fall out even when you hold the puzzle vertically, and the moves feel more controlled and “solid”.
• Durable ABS body. The rigid plastic makes the puzzle feel heavy and solid, designed for active play and frequent use.
• Clear, long-lasting print. The numbers are printed neatly and with high contrast; they do not fade or rub off during normal use.
• Compact format. The size is about 15 × 18 × 1.9 cm, which makes it easy to take with you on trips, to classes or to school.

Math tasks and learning

The classic 15-puzzle is not just a game, but also a very visual mathematical model. With this puzzle it is easy to explain to children the ideas of permutations, parity, invariants and even take first steps towards group theory.

On the basis of QiYi Kiotski 4×4 you can build a whole set of tasks:

Basic level (primary school):

• arrange the numbers in order while counting the number of moves out loud;
• hold a mini-contest: “who can do it in fewer moves”;
• tasks like “solve only the first row”, “put numbers 1–8 in the correct order, the rest can be ignored”;
• simple arithmetic problems: calculate the sum of numbers in a row or column, find “neighbors” by value (numbers that differ by 1 or 2).

Intermediate level (logic and combinatorics):

• discuss how many different arrangements of numbers there can be at all, and why some states are fundamentally unreachable by legal moves;
• look for strategies: come up with and describe an algorithm for always solving the first row or the first two rows first;
• run “experiments”: record time and move counts, build tables of results and compare strategies.

Advanced level (math clubs and older students):

• introduce the concept of inversions in a permutation: count how many pairs of numbers are “out of order” and track how this number changes with each move;
• introduce the idea of an invariant: show that there is a combination of position characteristics (for example, the parity of the permutation plus the position of the empty cell) that does not change under any legal move;
• offer problems like “prove that this particular configuration cannot be solved” — an excellent example of a strict yet accessible mathematical proof based on a familiar toy.

These tasks develop not only the skill of solving the puzzle, but also mathematical thinking: analyzing states, looking for patterns, formulating and testing hypotheses. That is why 4×4 sliders are often recommended as mathematical puzzles for children and teenagers.

Who this puzzle is for

• for school-age children as a first logic game for planning moves and counting;
• for adults as a compact “anti-stress” puzzle and logic trainer;
• for speedcubing enthusiasts as an alternative “speed solving” format and finger warm-up;
• for clubs, math circles and schools as a visual aid for topics like permutations, parity, invariants and small research projects in mathematics.

Main specifications

• Brand: QiYi (QY Toys / MoFangGe)
• Model: Kiotski / Number Klotski 4×4, code EQY709
• Type: sliding puzzle (“15-puzzle”)
• Grid: 4×4, 15 numbered tiles + one empty space
• Magnets: yes, in the base and/or tiles
• Material: ABS plastic
• Approximate size: 15 × 18 × 1.9 cm
• Age: approximately from 6 years (when playing with children, under adult supervision).