10 people use a contact tracing app. It shows that each user has been in close contact with exactly four other users and indirectly exposed to the other ve users. Person 1 becomes ill and Person 2 wants to measure how much he is at risk. He uses the app to find the smallest value of k for which there exist people P1, . . . , Pk such that Person 1 has been in close contact with another person , person Pi has been in close contact with person Pi+1 for i = 1, . . ., k 1 and person Pk has been in close contact with person 2. Determine the largest possible value of k and prove that your answer is correct