Leveling up and Getting Items! v2

Question

This is follow up question to Leveling up and Getting Items!

You are playing an online RPG game with 9 friends of yours (10 people in total) and in the game, there is a 2-player dungeon where you level up every time you enter and complete it. Only up to two players are allowed inside it at a time. At the beginning of the game, everybody is level 1 as usual. Before the game released, there was a beta and you know how to level up fast from it, but there are some tricks you discovered.

• You cannot complete the dungeon alone.
• After completing this 2-player dungeon with your friend, you and your friend will get 1 level.
• If you play the dungeon with someone exactly one level below you, you will get an extra item at the end of the dungeon, but you cannot enter the dungeon with a friend more than one level below you.
• If you try to enter the dungeon with the same person again, no one will get any experience to level up or item.
• You can share the items later, they are not soulbound!

There is a patch happened today! I do not want to bother you with the whole patch notes but the most important part is as below:

• If you play the dungeon with someone exactly one at most 2 levels below you, you will get an extra item at the end of the dungeon, but you cannot enter the dungeon with a friend more than one level two levels below you.

So

Does this patch change anything? we did not start to play yet, can we get more than 40 items?

Answer 1

It changes a lot!

Building off the logic of my answer to part 1, "cycles" were limited in that players could only be in them twice (excepting the weird "5-apart" cases). With your added rule, players can be in a cycle 3 times, allowing us to do a lot more than we did before. The first and 45th pair are still hopeless, so the answer is 43 extra items

[2,3] [3,4] [4,5] [5,6] [6,7] [7,8] [8,9] [9,10] [10,1]
[1,4] [4,7] [7,10] [10,3] [3,6] [6,9] [2,5] [9,2] [5,8] [8,1]
[1,3] [2,4] [3,5] [4,6] [5,7] [6,8] [7,9] [8,10] [9,1] [10,2]
[1,6] [6,2] [6,10] [10,5] [10,4] [4,9] [4,8] [8,3] [8,2] [2,7]
[1,5] [5,9] [3,9] [3,7] [7,1] [1,2]

That looks really confusing. There a nicer way to do charts in here? This is why I usually do screen captures of excel. As for the order I chose, I didn't try too hard, it just sort of fell together at the end. I'm sure there are many solutions at 43.