IBM Ponder This #236 · December 2017

Recently, IBM announced the free Quad-9 service to protect your computer systems. This reminded us of the six degrees of separation idea that claims that every two people are no more six acquaintances apart when counting the minimal length of a chain of friends connecting them.
Of course, one can create a world where this rule does not hold.

Let's assume that our (small) world has only 100 people, and every one of them knows exactly nine other people, and that knowing someone must be symmetrical (i.e., a knows b if and only if b knows a).

What is the largest diameter of this connection graph?

To be listed as a solver - send us a possible "knowing graph" where there are at least two people whose shortest chain is 27 hops long.

Number the people from 1 to 100 and list the solution in 100 lines of nine numbers each.

There is a solution for a world of 12 people in which each person knows exactly three others with a chain length of six hops. However, to clarify the format, here is an example of that 12-person world with a maximum chain of three hops (the first line means that #1's friends are 2,7,12; the last line means that #12's friends are 1,6,11):

2 7 12
1 3 8
2 4 9
3 5 10
4 6 11
5 7 12
1 6 8
2 7 9
3 8 10
4 9 11
5 10 12
1 6 11

Solution

Best opened after a real attempt

To be added.