The engines are used for Tayam, Luminous Enigma activations, as such many of them use the vigilance counters he provides. Many of the engines also use Ashnod's Altar or Phyrexian Altar these are used to completely power the ability. You can use another sac outlet to make a "counters only" version of the engine when digging for other pieces. If you are able to establish a counters only engine Lotus Bloom can provide mana until you find all of the pieces to a line that will return other cards.
Tayam, Luminous Enigma, Ashnod's Altar, and Caller of the Claw: Requires 4 of your creatures to have died this turn, or 3 additional mana and 2 of your creatures to have died this turn to start. Caller of the Claw enters with a vigilance counter and creates 2/2 bear tokens equal to the number of creatures that have entered your graveyard this turn that each enter with a vigilance counter. Sacrifice creatures until you have 3+ mana. Activate Tayam, Luminous Enigma removing counters from among the tokens and Caller, if you do not have at least three counters left among your creatures and Caller was not one of the creatures you sacrificed for mana, sacrifice it in response to Tayam. If Caller is in the graveyard return it with the Tayam activation, otherwise return one of your other permanents CMC 3 or less.
Tayam, Luminous Enigma, Phyrexian Altar, and Caller of the Claw: Requires 5 of your creatures to have died this turn, or 3 additional mana and 2 of your creatures to have died this turn to start. Caller of the Claw enters with a vigilance counter and creates 2/2 bear tokens equal to the number of creatures that have entered your graveyard this turn that each enter with a vigilance counter. Sacrifice creatures until you have 3+ mana. Activate Tayam, Luminous Enigma removing counters from among the tokens and Caller, if you do not have at least three counters left among your creatures and Caller was not one of the creatures you sacrificed for mana, sacrifice it in response to Tayam. If Caller is in the graveyard return it with the Tayam activation, otherwise return one of your other permanents CMC 3 or less.
Tayam, Luminous Enigma, Ashnod's Altar, and Hallowed Spiritkeeper: Requires 2 creatures in your graveyard and 1 mana to start. Sacrifice Hallowed Spiritkeeper making 2 additional mana. Hallowed Spiritkeeper will make tokens equal to the number of creature cards in your graveyard that each enter with a vigilance counter. Activate Tayam, Luminous Enigma removing counters from among the tokens. Return Spiritkeeper with the Tayam activation. Sacrifice Spiritkeeper and/or tokens for mana. Once you have more than 2 other creatures in the graveyard you will not have to sacrifice Spiritkeeper unless you need more counters to keep the engine going. At this point you can start returning other permanents CMC 3 or less.
Tayam, Luminous Enigma, Phyrexian Altar, and Hallowed Spiritkeeper: Requires 2 creatures in your graveyard and 2 mana to start. Sacrifice Hallowed Spiritkeeper making an additional mana. Hallowed Spiritkeeper will make tokens equal to the number of creature cards in your graveyard that each enter with a vigilance counter. Activate Tayam, Luminous Enigma removing counters from among the tokens. Return Spiritkeeper with the Tayam activation. Sacrifice Spiritkeeper and/or tokens for mana. Once you have more than 2 other creatures in the graveyard you will not have to sacrifice Spiritkeeper unless you need more counters to keep the engine going. At this point you can start returning other permanents CMC 3 or less.
Tayam, Luminous Enigma, Ashnod's Altar, and Weaponcraft Enthusiast: Requires 3 mana to start. Make the tokens with fabricate. Weaponcraft Enthusiast and each token will enter with vigilance counters. Activate Tayam, Luminous Enigma removing the three counters. In response sacrifice Enthusiast, then tokens until you have 3 mana. Return Enthusiast with the Tayam activation. This engine will not return any other permanents. It is used to find one of the other engines and then you leave Enthusiast in the graveyard and start the other engine.
Tayam, Luminous Enigma, Phyrexian Altar, and Weaponcraft Enthusiast: Requires 3 mana to start. Make the tokens with fabricate. Weaponcraft Enthusiast and each token will enter with vigilance counters. Activate Tayam, Luminous Enigma removing the three counters. In response sacrifice Enthusiast, then tokens until you have 3 mana. Return Enthusiast with the Tayam activation. This engine will not return any other permanents. It is used to find one of the other engines and then you leave Enthusiast in the graveyard and start the other engine.
Tayam, Luminous Enigma, Ashnod's Altar, and Promise of Bunrei: Requires 1 creature on board and 1 mana to start. Sacrifice the creature for mana triggering Promise of Bunrei. Four tokens are created and enter with vigilance counters. Activate Tayam removing three of the counters. Return Promise with the Tayam activation. Sac tokens until you have three mana, triggering Promise again. Once you have enough extra tokens with vigilance counters on them you can return other stuff with Tayam and leave Promise in the graveyard until you need counters again.
Tayam, Luminous Enigma, Phyrexian Altar, and Promise of Bunrei: Requires 1 creature on board and 2 mana to start. Sacrifice the creature for mana triggering Promise of Bunrei. Four tokens are created and enter with vigilance counters. Activate Tayam removing three of the counters. Return Promise with the Tayam activation. Sac tokens until you have three mana, triggering Promise again. Once you have enough extra tokens with vigilance counters on them you can return other stuff with Tayam and leave Promise in the graveyard until you need counters again.
Tayam, Luminous Enigma, Ashnod's Altar, and any two persist and/or undying creatures: Sacrifice the two recursion creatures for mana. Each will return with a vigilance counter and a counter from its ability. Activate Tayam, Luminous Enigma removing one vigilance counter and the two from the abilities.
Tayam, Luminous Enigma, Phyrexian Altar, and any three persist and/or undying creatures: Sacrifice the three recursion creatures for mana. Each will return with a vigilance counter and a counter from its ability. Activate Tayam, Luminous Enigma removing the three from the abilities.
Tayam, Luminous Enigma, Ashnod's Altar, Luminous Broodmoth, and any two non-flying creatures: Sacrifice the two non-flying creatures for mana. Each will return with a vigilance counter and a flying counter. Activate Tayam, Luminous Enigma removing one vigilance counter and the two flying counters.
Tayam, Luminous Enigma, Phyrexian Altar, Luminous Broodmoth, and any three non-flying creatures: Sacrifice the Three non-flying creatures for mana. Each will return with a vigilance counter and a flying counter. Activate Tayam, Luminous Enigma removing the three flying counters.
Tayam, Luminous Enigma, Ashnod's Altar, Mikaeus, the Unhallowed, and any two non-human creatures: Sacrifice the two non-human creatures for mana. Each will return with a vigilance counter and a +1/+1 counter. Activate Tayam, Luminous Enigma removing one vigilance counter and the two +1/+1 counters.
Tayam, Luminous Enigma, Phyrexian Altar, Mikaeus, the Unhallowed, and any three non-human creatures: Sacrifice the Three non-human creatures for mana. Each will return with a vigilance counter and a +1/+1 counter. Activate Tayam, Luminous Enigma removing the three +1/+1 counters.
Tayam, Luminous Enigma, Devoted Druid, and Gift of Granite: Tap Devoted Druid for mana. Put a -1/-1 counter on it to untap it via its ability. Repeat 3 times. Activate Tayam by removing the -1/-1 counters.
Tayam, Luminous Enigma, Devoted Druid, Luminous Broodmoth, Thousand-Year Elixir: Tap Devoted Druid for mana. Put a -1/-1 counter on it to untap it via its ability. Tap Devoted Druid for mana. Put a -1/-1 counter on it via it's untap ability. Devoted Druid dies and is returned with a flying counter and a vigilance counter. Tap Devoted Druid for mana. Put a -1/-1 counter on it to untap it via its ability. Activate Tayam removing the flying, vigilance, and -1/-1 counters.
