The Mongols were not undefeated and certainly not invincible. However, in order to beat the Mongols one had to be clever, organized, timely and lucky (or any combination thereof). As history has shown, only a select few enemies of the Khans possessed displayed any of those traits. The Khwarazmian Empire and Mamluks proved the Mongols could be beaten in grand fashion. I am unfamiliiar with the methods used by the Khwarazmian army but the Mamluks at the battle of Ain'Jalut simply beat the Mongols at their own game; they used cunning (feint tactics followed by a counterattack) and blisteringly effective horse archery.
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