IBM Ponder This #253 · May 2019

Several people want to cross a river from one bank to the other using a boat that can carry at most two people.
There are some restrictions on who can be left on the bank, and the travelers want to use as few boat trips as possible.
Your task this month is to discover the restrictions on eight people that will make the shortest solution at least 73 trips long.

Here's a simpler example of this problem: Let's say you wanted to move six people from one river bank to the other, with the stipulation that the shortest solution includes at least 11 boat trips. This scenario could include three parents (A, B, C) and their respective children (a, b, and c respectively), when no child is willing to stay on either bank of the river with any other parent unless his or her own parent is also present on the same bank.

Please supply your answer as a 32-digit hexadecimal number that represents 128 bits: one for each possible subset of seven people that cannot be on the same river bank with the eighth person.

To exemplify the format, here is the six-person example presented above in this format:
The legal subsets of people include the following 22 sets:

...... abcABC
...ABC abc...
.bcABC a.....
a.cABC .b....
ab.ABC ..c...
.bc.BC a..A..
a.cA.C .b..B.
ab.AB. ..c..C
a..ABC .bc...
.b.ABC a.c...
..cABC ab....
11 of them contain "a":
abcABC
abc...
ab.ABC
ab.AB.
ab....
a.cABC
a.cA.C
a.c...
a..ABC
a..A..
a.....

This corresponds to the indices 31, 24, 23, 22, 16, 15, 13, 8, 7, 4, 0. Since we asked for 1 bit for every illegal set, the binary number has zeros in these places, so it is 01111110001111100101111001101110, which is, in hexadecimal: 7e3e5e6e.
By the way, there is a better solution for six people that requires 19 boat trips. What is it?

To give yet another example, for eight people, the hexadecimal number 4672616e63657320452e20416c6c656e yields a shortest path of length 13.

Bonus question: a name is hidden in the last example; she is the sixth in a list of 19 people (till today). Can you list them all?

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Update (27/5): Since May's challenge was harder than usual - we are giving one more month to solve it.

Solution

Best opened after a real attempt

To be added.