Nothing complicated... Question 1: Is this a Basic, Advanced, or Expert game? (Even though Shaks can't acquire Water Magic normally, and Water Magic isn't available in the barracks randomly, a Mage can provide it...) Question 2: Are Trolls buffed or not? Question 3: Underground/Grass/Neutral terrain?

Basic Trolls: Attack 4, level 1-3. Buffed Trolls: Attack 5, level 1-3. Basic Bless: Deals 3 damage, higher Bless deals 4. Gnomes (unbuffed/buffed): Defense 7. Shak, level 1: Attack 2, -10% bonus to Troll attack. Shak, level 3: Attack 4 (as per the condition), 30% bonus to Troll attack. Shak, level 5: +1 attack bonus.

Let's take a Basic Bless, unbuffed Trolls, and neutral terrain. (For buffed Trolls, it's +1 attack; for underground, it's another +1 attack; for grass, Gnomes get +1 defense).

The calculation is as follows: Total damage = damage * quantity * (1 + difference (attack - defense) + bonus).

Calculation: Case 1: Troll attack 7 (4 base + 2 from Shak + 1 Shak bonus) - Gnome defense 7, so there's no difference. Therefore, the damage is simply (1-3) * quantity * 1.1 (bonus), and empirically, Trolls deal 1.7-2.3 damage per unit.

Therefore, to defeat 600 hit points of 30 Gnomes, you need at least: 1.7 * quantity * 1.1 = 600, so quantity = 321 Trolls. If we assume the average Troll damage is exactly 2, then you need 600 / 2.2 = 273 Trolls.

Case 2: Green Shak attack = 9 (4 + 4 + 1), so the damage formula = (1-3) * (1.1 (attack-defense difference) + 0.3 (bonus)) * quantity. Therefore, with a minimum of 1.7 damage per unit, quantity = 600 / 1.4 / 1.7 = 253. For 2 damage, quantity = 600 / 1.4 / 2 = 215.

Case 3: Everything remains the same, the Troll attack hasn't changed (the attack bonus is only at level 6, +2), so only the damage has changed - it's now 3. Therefore, quantity = 600 / 1.4 / 3 = 143.

For buffed Shaks, instead of 1.4 (1.1 in the first calculation), it will be 1.45. For unbuffed Shaks on their own terrain, it's also 1.45, and for buffed Shaks on their own terrain, it's 1.5. If the Gnomes are on grass, the calculation for basic Trolls becomes more complicated, as it will be 1 - 0.025 + bonus, and for buffed Trolls, it's simply 1 + bonus.

It's all quite simple...