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When you activate (flip face-up) a Continuous Trap Card that has a Quick-like Effect, you can choose to activate that effect; in this case, the Quick-like effect does not create an additional Chain Link. You simply state if you will also activate the effect of the Continuous Trap Card at the same time you activate the card itself. If the Continuous Trap Card is already face-up on the field, you can activate it in a new chain, or chain its effect to another card, similar to Quick Effects of monsters. Quick-like Effects can be activated during either player's turn.
Example 1: Player A activates "Mystical Space Typhoon" and targets Player B's set "Cyber Network"; Player B activates "Cyber Network" and chooses to activate its effect, banishing 1 LIGHT Machine-Type monster from his/her Deck.
"Cyber Network" resolves first and banishes a monster, then it is destroyed by "Mystical Space Typhoon" and its second effect is activated, Special Summoning the banished monster.
Example 2: Player A Normal Summons "Steelswarm Hercules"; Player B activates "Bottomless Trap Hole". Player A activates "Infestation Infection" and chooses to activate its effect, shuffles "Steelswarm Hercules" into the Deck and searches for another "Iswarm" monster.
"Infestation Infection" resolves first and prevents "Steelswarm Hercules" from being banished by "Bottomless Trap Hole".
Example 3: Player A activates "Pot of Dichotomy" and targets 3 monsters in the Graveyard to be shuffled into the Deck; Player B activates "Sealing Ceremony of Suiton" and also activates its effect, discarding a WATER monster and banishing one of the monsters "Pot of Dichotomy" targeted.
"Sealing Ceremony of Suiton" resolves first, banishes one of the 3 monsters targeted by "Pot of Dichotomy", and the latter's effect fades out.