## 3 Results
### Technical Parameter Mapping of Elderly Game Products
To further verify the effectiveness of the proposed solution in improving product acceptance, the existing \"Jike\" brand electronic building block puzzle toy in the market was selected as a sample solution, as shown in Figure 11. A panel comprising 26 elderly-friendly product design experts, 23 game product designers, 24 scholars in related fields, and 29 elderly users scored the solutions on a 7-point Likert scale. After standardizing the results, the initial evaluation matrix F was compiled, as shown in Equations (27)-(30). The relative closeness of each solution was calculated based on the scores of the four user groups. \[F_{1}=\left[ \begin{array}{cccccc}5.1&4.4&4.5&5&4.5\\ 5.2&4.3&4.8&5.1&4.7\\ 4.8&4.2&4.6&4.8&4.6\\ 4.5&4.1&4.2&3.9&4.3\\ \end{array} \right]\]  
\[F_{3}= \begin{bmatrix}5.2&4.7&4.9&4.8&4.8\\ 5.2&4.8&4.9&5.1&5\\ 5.2&4.9&4.8&4.8&4.9\\ 4.7&4.6&4.5&3.9&4.7\\ \end{bmatrix}  \tag{29}\]  
\[F_{4}= \begin{bmatrix}5.2&4.7&4.6&4.9&4.4\\ 5.4&5&4.6&4.9&4.8\\ 4.9&4.9&4.7&4.7&4.7\\ 4.3&4.2&3.8&4.2&4.5\\ \end{bmatrix}  \tag{30}\]  
The relative closeness of each solution was calculated based on the scores of the four user groups. The results are shown in Figure 12.  
Solution 2 had the highest relative closeness value, confirming that it was the optimal choice. Conversely, the existing market design ranked the lowest, demonstrating the reliability of this study's design pathway for elderly-friendly game products. To verify the stability of the rankings generated by the TOPSIS method, 15 product designers and older adults were invited to jointly evaluate alternatives using the GRA method. Centered on the five thematic topics extracted from the BTM model and the design schemes, the solutions were evaluated using a 5-point Likert scale. In GRA, a higher grey relational grade indicates a better alternative. As shown in Table 9, a comparison between the two methods revealed that solution 2 consistently ranked as the top solution, confirming the stability and reliability of the TOPSIS results. Figure 11: Electronic block puzzle toy by Jike. Figure 12: Relative closeness results for evaluated solutions. To prevent resource waste during production and development, the optimal solution was further refined, as shown in Figure 13. The gameplay mechanism in Solution 2 involved controlling the rotation of a block within a defined space, with players navigating the block along a light-guided trajectory. The objective was to position the orange face of the block at the designated endpoint within a specified time frame. This design trains the players in terms of spatial and logical thinking. Upon winning, the system played a congratulatory sound to boost emotional engagement and encourage continued play. Players can use a single finger to control the movement of a block in four directions (up, down, left, and right), ensuring ease of use for elderly users. In case of errors, the system provides immediate feedback with a \"ding\" sound to help players identify and correct their actions. A detailed gameplay flowchart is shown in Figure 14. To enhance the gaming experience, block props can be modularly combined, increasing interactivity and difficulty in boosting engagement and enjoyment. Players can adjust their difficulty by rotating a dial, offering personalized options to suit various skill levels. Solution 2 was 20 cm long, 15 cm wide, and 2 cm high, making it compact and lightweight. The block props were designed as 2 \(\times\) 2 cm cubes, an ergonomic size for elderly users to grip and operate. To improve safety, the product should have a simple geometric shape with rounded chamfers. Many older adults experience high-frequency hearing loss, particularly reduced sensitivity to sounds above 4000 Hz [30]. According to ISO 7029, individuals over the age of 65 exhibit a significant decline in high-frequency auditory perception [31]. To enhance audibility, the product's audio frequency range was set between 500 and 3000 Hz, covering the core range of human speech and better suited to elderly users.