A derangement avoids self-gifts
A Secret Santa assignment is a directed cycle: each participant gives to one different recipient and receives from one different giver. For six names, the construction rotates a shuffled order, so self-assignment is impossible and nobody is assigned twice as a recipient. The important condition is not simply random names; it is a one-to-one mapping with no fixed point.
Following a six-person cycle
Suppose a shuffled cycle is Alex → Drew → Finley → Blair → Emery → Casey → Alex. Alex buys for Drew, Drew for Finley, and Casey closes the loop by buying for Alex. Every person has exactly one recipient and one giver. If Alex learns Drew's name, that does not reveal the entire cycle, although informal sharing can leak links through the group.
Privacy depends on delivery
The mathematical assignment is only one part of a gift exchange. Displaying all pairings on a shared screen defeats the secrecy requirement even though the permutation is valid. Send or reveal each recipient privately, agree on a spending limit, and decide whether exclusions such as household members are needed before generating the cycle.
Constraints beyond no-self
This simple method does not prevent partners, siblings, or coworkers from drawing each other, and it does not enforce wish lists or shipping addresses. Repeatedly redrawing after discovering an unwanted pairing can bias the procedure and confuse the record. A constrained matching system is necessary when prohibited pairs matter; this tool covers only the no-self rule.
Keep the exchange workable
A valid no-self mapping does not guarantee that every gift can be delivered. Confirm the exchange date, spending limit, address or meeting arrangement, and whether participants may decline. If somebody withdraws, regenerate or use a documented reassignment method rather than revealing all recipients to repair one link. The cycle is a useful private structure for a voluntary activity; it is not a justification for collecting unnecessary personal details.
Decide how recipients stay private
Confirm the voluntary participants and privacy method before recipients are assigned or any exchange information is shared.
Gift-cycle questions
Can someone draw themselves?
No. The cyclic assignment gives every participant a different recipient.
Does it block couples?
No. Household or relationship exclusions require a constrained matching rule.