Thus, when it was discovered that the Prussians had somehow concentrated more quickly (due to treason, the concentration began the night of the 14th) this offered Napoleon an opportunity to destroy one of the allied armies.
I am always a bit uneasy to say the Prussians or Wellington's army, which in fact in my view acted as one - hence eye witnesses remarks speaking of the left wing of their army - meaning the Prussians, or even Napoleon speaking early at the 16th more or less of one army.
Blücher accepted battle initially due to the idea that Wellington would support him and in the end took on Napoleon on his own, which is the popular view, but the right wing (Wellington) tied a lot of French units at QB - which enabled more or less an orderly withdrawel of the Prussians (left wing), keeping their army despite all heavy losses in fighting shape.
Wellington accepted battle at the 18th because he was assured by Blücher that he will not only support him by one corps but the whole army.
Napoleon didn't anticipate that Wellington would confront him, therefore his joy that he did so. Napoleon did not reckon with the Prussians for another one or two days. An alarm bell should have rung - when Wellington did offer battle (indicating indirectly that some re - inforcements must be on Wellington's way).