Passing the county exam was once called 'entering the pàn.'
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The 泮宫 was the school of a Zhou-era feudal lord, named for the crescent pool (泮水) in front of it. 'Entering the pàn' (入泮) later became a phrase for a young scholar passing the entry-level imperial exam.
Three-drop water radical, the side-form of 水. It points to the crescent moat-pool that surrounded the academy, and to the 'thaw' sense (ice turning to water).
Right side 半 gives the sound (bàn → pàn) and a fitting hint of 'half' — the academy pool was a half-circle, not a full ring. Same phonetic in 判 to judge and 叛 to betray.