(1) A Gnutella topology looks like a balanced ternary tree with 4 levels of nodes, i.e., peers, as shown in the picture below. Thus, there is 1 root at Level 1, which has 3 children at Level 2, which each have 3 children at Level 3, which in turn each have 3 children at Level 4 – thus, there are a total of 40 nodes.

If the root node (Level 1) sends a Query message with TTL=2, then what are the number of nodes receiving the Query message, not including the originating node?

(2) A Gnutella topology looks like a balanced ternary tree with 5 levels of nodes, i.e., peers. Thus, there is 1 root at Level 1, which has 3 children at Level 2, which each have 3 children at Level 3, which in turn each have 3 children at Level 4, which in turn each have 3 children at Level 5 – thus, there are a total of 121 nodes.

If a leaf (Level 5) node sends a Query message with TTL=2, then what are the number of nodes receiving this message, not including the originating node?

(3) A Gnutella topology looks like a balanced ternary tree with 4 levels of nodes, i.e., peers, as shown in the picture below. Thus, there is 1 root at Level 1, which has 3 children at Level 2, which each have 3 children at Level 3, which in turn each have 3 children at Level 4 – thus, there are a total of 40 nodes.

If a child of the root (i.e., a Level 2 node in the tree) sends a Query message with TTL=3, then what are the number of nodes receiving the Query message, not including the originating node?

(4) A Gnutella topology looks like a balanced ternary tree with 4 levels of nodes, i.e., peers, as shown in the picture below. Thus, there is one root at Level 1, which has 3 children at Level 2, which each have 3 children at Level 3, which in turn each have 3 children at Level 4 – thus, there are a total of 40 nodes.

If the originating node of the Query is a leaf (Level 4 node), what is the minimum TTL to ensure all nodes in the system receive the Query?