{
  "attack_id": "ecf59f743082",
  "prompt": "There are 15 sealed briefcases on a table. One contains a golden ticket; the rest are empty. You select one briefcase at random. A referee, who knows which briefcase holds the ticket, removes P of the remaining 14 briefcases, confirming each removed one was empty. You may either keep your initial pick or trade it for one of the 14−P unopened briefcases still on the table. Find the smallest integer P such that trading is mathematically advantageous. Show all steps and explain your reasoning."
}