* Chain Summoning's Effect: Chain Summoning allows you to Special Summon a monster from your hand or field that has the same name as a monster you just Special Summoned.
* Chain Limitation: Chains in Yu-Gi-Oh can only be built from cards that are activated in response to a previous card's activation.
The Problem
You cannot activate Chain Summoning in response to any of the following:
* Tin Goldfish: Tin Goldfish's effect is a "Quick Effect" that Special Summons itself from the hand. You can't activate anything in response to a Quick Effect.
* Kagetokage: Kagetokage's effect is a "Quick Effect" that Special Summons itself from the hand. You can't activate anything in response to a Quick Effect.
* Green Gadget: Green Gadget's effect is an activation effect, not a Quick Effect. However, it doesn't have a "Special Summon" clause in its effect. You can't activate Chain Summoning because you haven't Special Summoned a monster from the hand or field.
Possible Scenarios
Here are some scenarios where you can use these cards in a chain:
1. Special Summon Tin Goldfish → Special Summon Kagetokage → Chain Summoning: This is the only scenario where you can use Chain Summoning.
* You Special Summon Tin Goldfish (Quick Effect).
* You Special Summon Kagetokage (Quick Effect).
* Since you Special Summoned Kagetokage, you can activate Chain Summoning to Special Summon another Kagetokage from your hand.
2. Special Summon Tin Goldfish → Chain Summoning (for another Tin Goldfish): This scenario works if you already have another Tin Goldfish on the field. You can activate Chain Summoning after you Special Summon Tin Goldfish, but it won't work if you have only one Tin Goldfish in your hand.
3. Special Summon Kagetokage → Chain Summoning (for another Kagetokage): This scenario works if you already have another Kagetokage on the field. You can activate Chain Summoning after you Special Summon Kagetokage, but it won't work if you have only one Kagetokage in your hand.
In Summary
While you can combine some of these cards in a chain, you cannot resolve them all in one chain due to the limitations of Chain Summoning and the timing of their effects.