Combinatorics homework

Our first Combinatorics homework included three subjects. The first was difficult. After some deduction, the problem could be changed to be the following one. Let b1,b2,...,b77,b1+22,b2+22,...,b77+22 be different with each other, and equal to 1,2,...,154,respectively. The prblem is whether b1,b2,...,b77 exist. After some discussion with Xiaopeng Hong and Huipeng Zhang, I decided to simulate the process by some program. But when I finish it, the time computational complexity is too high to calculate.

However, if we list the possible sequence, there is some conflict. So the problem is with no answer.