Hide and Seek is a two-player game, played over a graph. The nodes of the graph are boxes in which tokens may be placed by one player, called Hider. The other player, called Seeker, seeks to find the location of the hidden tokens. Seeker travels across the graph along the edges and looks in each box as she reaches each node. This game is an abstract model for many cyber security domains, where Hider or Seeker might be a malicious actor. Suppose there are 12 nodes, arranged in a circle; thus, each node has two direct neighbours. The nodes are numbered 1, 2, 3, ..., 12 (as on a clockface). The Hider places 3 tokens in 3 different boxes on the graph. The Seeker knows that she has to find 3 tokens, but she does not know at which nodes they are hidden Seeker always starts at node 12 and she proceeds to search along the graph, going either clockwise or anti-clockwise. Here are three questions. Which statement has the correct answers for all three questions in order? (a) What is the maximum number of nodes Seeker has to search in order to identify the locations of all three tokens? (b) Suppose Seeker searches 9 nodes without finding a token. What is the maximum number of additional nodes she needs to search in order to identify the locations of the tokens? (c) Assume there is a cost for searching, and this cost is the same for each link traversed. If Seeker always travels anti-clockwise, at which nodes should Hider place the tokens in order to maximize the search costs to Seeker? a. (a) 12 (b) 0 (c) Place the tokens in Boxes #1, 2 and 3. b. (a) 11 (b) 0 () Place one token in Box #1 and no token in Box #2. The other two tokens can be placed anywhere. OC (a) 12 (b) 0 (c) Place one token in Box #1 and the other two tokens anywhere. d. (a) 11(b) 0 (c) Place the tokens anywhere. e. (a) 11 (b) 0 (c) Place the tokens in Boxes #1, 2 and 3