—According to legend, Gordius was a Greek king.  He tied an extremely complex knot, and an oracle prophesied that whoever untied it would rule all of Asia. 
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—Alexander the Great “untied” the knot simply by cutting through it with a sword.

—A “Gordian Knot” is any extremely complex problem, and “cutting the Gordian Knot” refers to solving such a problem in a quick decisive manner.
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—Example: Each year the school counselors face the Gordian knot of scheduling classes.
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—Example: The councilwoman cut the Gordian knot so that two worthy programs would not have to be cut.  Cutting both programs budgets prevented from having to eliminate one or the other.

—In the Gospels, Judas Iscariot was the disciple who agreed to betray Jesus to the authorities in exchange for payment. The thirty pieces of silver were the price of Judas’s betrayal. The way Judas identified Jesus for the authorities was to approach and greet him with a kiss of identification. 
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“Thirty pieces of silver” refers to payment received for an act of treachery.

—“Betrayed with a kiss” refers to a supposed friend’s treachery.
 
Example: Patrick Henry warned his listeners about the supposed friendliness of the British.  He warned, “Suffer not yourselves to be betrayed with a kiss.”

Example: When the senator abruptly changed his vote to support the wealthy developer’s project, some of his colleagues muttered that he would probably receive his thirty pieces of silver from the developer.