Nerdle: use equation structure to eliminate possibilities

Nerdle becomes a precise elimination puzzle once equation syntax is treated as information. An opening guess should sample several digits and both common operators while remaining mathematically valid. After the feedback, preserve the equality balance, apply operator precedence and test whether repeated digits or operators are still possible; a colored tile does not always mean the symbol appears only once. The most useful post-round explanation would show why candidate equations were excluded. That teaches arithmetic structure instead of rewarding blind enumeration.