What would be your MOST ANNOYING GYM?
What would be your most annoying/surprising line up or defenders?
Let's say you attack the lowest defender, a DT/HP Gyarados with a Jolteon. Then the next defender is a MS/EQ Rhydon. You have a charged Thunderbolt but then it will be NVE against Rhydon plus Rhydon hits Jolteon SE with ground moves. So you'll switch to likely Vaporeon or Exeggutor. And the next defender is Exeggutor... Considering the laggy switch, you'll get hit by the first few quick attacks. Obviously, no gym is unbeatable, the aim here is to find the most annoying tower. Clearly the most annoying gym would be 10 ZHDG Blisseys, so let's say the rule is 2 of the same pokemon per tower.
What's your list from bottom to top? E.g: 1. DT/HP Gyarados, 2. MS/EQ Rhydon, 3. C/SoB Exeggutor, etc.
Edit: We've seen a couple of great solutions here, thanks.
I'll refine the criteria: first encounter (you don't know the defenders' moveset) and try to use specialist instead of a generalist.
Answers
According to your criteria...
2 Blissey
2 Snorlax
2 Vaporeon
2 Lapras
2 Steelix
Mathematically this is the most time consuming gym out of all the defenders in the game, that fits your criteria. (If you see the charts around this website you will find that these prolong the battles the most, but not necessarily deal the most damage to the attacker)
10 Blissey may be more of a chore in the actual fighting but then you can forget about your team selection bit because your Blissey attacking team is probably one you can recite...I've used mine for countless times allready and most likely, these pokemon will be at the top of your CP selection. Most time consuming yes, but certainly not as much mental effort.
I like Lapras as a defender. I really wish it had bubble or something though. I see a few out of town and they're always all ice or all water. So first time through I have to walk carefully but the second time through it is getting melted by a Dragon or a Tyranitar. If he could mix bubble/ice move though that would change. That would be real pain. I don't really understand why Lapras got an offensive water quick move when a good water move would have been great on D and watergun is hot garbage for Lapras.
To your hypothetical tower I'd take at least two Grass attackers and something with Bite for the Egg. Or just fight Gary with Gary for neutral damage, and since all 5 of mine have Bite the matter is just not taking the HP one. Or maybe take all the Garys, the HP one for Rhydon, Bite is just an energy builder anyway. The point is, if a gym is diverse, take most neutral attackers.
I'd take mons from the different combat triangles. Gyarados, Rhydon, Exeggutor, Vaporeon, Snorlax, Espeon, Blissey, Dragonite, Tyranitar, Tyranitar.
You start with a Jolteon to combat Gary? Too bad, Rhydon resists electric. Switch to Grass/Water? Too bad, next is Exeggutor, resists water, is grass type. Switch to Flareon? Next is Vaporeon. Then you're faced with a tank Snorlax. You switch to Heracross/Machamp? Next is Espeon, dealing super effective to fighting. And if you somehow manage to navigate through them, I still have a tank Blissey, a Dragonite, and 2 T-rexs. Get rekt.
:P
I would like to just kick the Gyarados out.
Then clear the Rhydon with ice Pokémon or something, as long as it doesn't have SE or RS. It can beat the Exeggutor, if I could find a Lapras somewhere. Vaporeon and Snorlax, just use Exeggutor and completes; unless the Vaporeon has Hydro Pump, where the dodge bug is annoying; if against a BS Snorlax, maybe SoB can't be used safely in the battle; backup will be Venusaur.
Espeon, simply switch to Umbreon.
Then runs away, Blissey will probably be too hard to beat.
Assuming gyms could be stacked in any order and not ordered by CP and the objective is to full sweep the gym, not just take out the bottom defenders.
Blissey ZH+DG
Gyarados DT+C
Rhydon MS+SE
Blissey ZH+DG
Dragonite SW+DC
Exeggutor C+Se
Snorlax ZH+BS
Dragonite SW+DC
Lapras IS+IB
Snorlax ZH+BS
Just trying to make the attacker switch out after each battle. Multi bar moves to slow the attacker as much as possible since they can't use specials as frequently compared to against 1 bar defenders.
Plus with 2 Blissey and 2 Snorlax an attacker might not have space to fit in a counter for Gyarados and/or Rhydon, they'll need at least 2, maybe 3 attackers either being Dragonite, Tyranitar or Machamp.
"Let's say you attack the lowest defender, a DT/HP Gyarados with a Jolteon. Then the next defender is a MS/EQ Rhydon. You have a charged Thunderbolt"
In such situations, it's good to use generalists whose strength lies in great stats combined with a good moveset, rather than type counter specialists who can't take a hit well when switching out on the next defender..
Using your Gyarados -> Jolteon example, a Dragonite is likely to performing similarly to a Jolteon in this situation, since it resists HP. And if you can finish before HP, then you'll likely lose too little HP to make much difference. Dragonite also resists Rhydon's EQ, which puts it on par with top water/grass types against Rhydon. I'd expect to have no problem quickly getting through both defenders without switching out, if I choose a generalist Dragonite.