The Secret Santa Assignment Algorithm

This tool uses a derangement algorithm to ensure no one gets themselves in the gift exchange. A derangement is a permutation where no element appears in its original position.

• Input Processing: Names are cleaned and duplicates are removed.
• Randomization: The list is shuffled using the Fisher-Yates algorithm.
• Assignment: Each person is assigned to give a gift to the next person in the shuffled list.
• Verification: The algorithm checks that no one is assigned to themselves.
• Output: Final assignments are displayed with optional spending limits and dates.

• Original: [Alex, Sam, Jordan, Taylor]
• Shuffled: [Taylor, Alex, Sam, Jordan]
• Assignments: Alex→Sam, Sam→Jordan, Jordan→Taylor, Taylor→Alex

The number of possible derangements for n items is given by the formula: !n = n! × Σ(from k=0 to n) of (-1)^k / k! For 5 people, there are 44 possible valid assignments where no one gets themselves.

Frequently Asked Questions

• How does the Secret Santa Name Picker work?

  The tool takes your list of names, shuffles them randomly, and creates a circular gift-giving arrangement where each person gives to someone else and no one gets themselves. It uses a derangement algorithm to ensure valid assignments.

• What if I have an odd number of participants?

  The algorithm works with any number of participants (minimum 3 for a proper exchange). Odd numbers work just as well as even numbers - everyone will still give and receive one gift.

• Can I exclude certain pairings (like partners or family members)?

  The current version creates completely random assignments. For exclusions, you would need to manually adjust the results or use a more advanced Secret Santa tool that supports exclusion rules.

• How random are the assignments?

  The assignments are generated using JavaScript's Math.random() function, which provides pseudorandomness suitable for this purpose. For cryptographic-level randomness, you'd need a different approach, but for Secret Santa, this is perfectly adequate.

• What happens if I run it multiple times?

  Each time you generate assignments, you'll get a different random result (unless by chance you get the same arrangement). You can generate multiple times until you're satisfied with the pairings.