## What is the fastest (non-spell) way to breach a castle wall?

A while back, my Pathfinder (1st edition) group was discussing late-game possibilities. I, playing a monk, noted that at 16th level my fists counted as adamantine for the purposes of overcoming damage reduction – I could literally punch holes in mountains, given a bit of time. I was reconsidering this conversation today and I got to wondering – what is the most efficient human siege weapon we can create?

So here’s the challenge: We are faced with a standard castle wall, 10 feet thick and made of stone (Per 3 feet of wall thickness: AC 2, hardness 8, 540 HP, Burst DC 50). We want to create a 20-foot-wide hole in the wall, in order to create a breach wide enough for soldiers to attack through. Since a wizard would have no trouble with this, we will be disallowing all spells and spell-like abilities (including those cast through an item). We’ll also ignore any siege weapons, excluding the PC themself. Everything else is valid, as long as it is official/published – supernatural and exceptional abilities, feats, magic weapons, and so on. How can we accomplish this in as few combat rounds as possible?

## Fastest algorithm to find all the possible paths of length $n$ from a give node in a directed graph?

I am trying to find the fastest algorithm to find all the possible paths of length $$N$$ from a given node in a directed graph.

My solution is to do a modification of breadth first search from the given node for $$N$$ iteration. Its time complexity is around $$\theta(V+E)$$. But the problem is $$|V|$$ & $$|E|$$ becomes exponential because as long as there is an edge, the same node can be visited again.

Can there be a solution of this problem with polynomial time complexity? It seems this problem has optimal substructure solution. Is there any solution using dynamic approach?

## What is the fastest path to an Ur-Priest Mystic Theurge

From the Complete Divine, the requirements for the Ur-Priest prestige class are:

• Any evil
• Base Saves: Fort +3, Will +3
• Skill Ranks: Bluff 6, Knowledge (arcana) 5, Knowledge (the planes) 5, Knowledge (religion) 8, Spellcraft 8
• Feats: Iron Will, Spell Focus (evil)

From the DMG, the requirements for the Mystic Theurge prestige class are:

• Skill ranks: Knowlege (arcana) 6, Knowledge (religion) 6
• Spells: Ability to cast 2nd level divine and 2nd level arcane spells.

The divine-side of the Mystic Theurge requirements can be fulfilled with 2 levels of the Ur-Priest class. Given at least 3 levels of an arcane caster class prior to entering Ur-Priest, what combination of base classes gives the fewest number of class levels in order to enter Ur-Priest? The 6 ranks of Bluff combined with a base Fortitude of +3 seem particularly difficult to acquire while still leaving room for at least 3 levels of an arcane caster.

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