Oracle Bone Inscriptions is one of the oldest existing forms of writing in the world. However, due to the great antiquity of the era, a large number of Oracle Bone Inscriptions (OBI) remain undeciphered, making it one of the global challenges in the field of paleography today. This paper introduces a novel approach, namely Puzzle Pieces Picker (P$^3$), to decipher these enigmatic characters through radical reconstruction. We deconstruct OBI into foundational strokes and radicals, then employ a Transformer model to reconstruct them into their modern (conterpart)\textcolor{blue}{counterparts}, offering a groundbreaking solution to ancient script analysis. To further this endeavor, a new Ancient Chinese Character Puzzles (ACCP) dataset was developed, comprising an extensive collection of character images from seven key historical stages, annotated with detailed radical sequences. The experiments have showcased considerable promising insights, underscoring the potential and effectiveness of our approach in deciphering the intricacies of ancient Chinese scripts. Through this novel dataset and methodology, we aim to bridge the gap between traditional philology and modern document analysis techniques, offering new insights into the rich history of Chinese linguistic heritage.