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http://teveclub.hu/naplo/
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Runesape
The funniest math problem in RuneScape:
I’ve often wondered – as I’m sure you have – just how dangerous TzTok-Jad is. Well, fellow warriors, wonder no more! Having spent decades of my life in battle with the most dangerous of creatures, and an equal amount of time calculating how many tinderboxes it would take to set Morytania alight, I can assuredly provide you with the theoretical results of the most epic battle never to have graced the Fight Cave of the TzHaar city: TzTok-Jad vs. Chickens!
Unfortunately, chickens are categorically incapable of hurting TzTok-Jad, so I’ve had to use roosters. Not quite the same, but amusing nonetheless.
The Situations
For simplicity’s sake, assume that TzTok-Jad can be swamped by any number of roosters, each of whom would be capable of pecking at him simultaneously. How many said roosters would be required for the mighty beast of magma to fall to a single peck from each rooster; that is, how many pecks does it take to defeat TzTok-Jad, ignoring any opportunity for him to regenerate or to call upon his Yt-HurKot henchmen?
More complexity. Assume that the roosters cannot stand upon each other’s heads, therefore leaving space for only 24 roosters to attack at any one time. Ignoring TzTok-Jad’s ability to regenerate, how long would it take those roosters to defeat him, and how many more would be required?
Finally, how many roosters must survive to the last wave of the Fight Cave to have a chance of defeating TzTok-Jad when his regeneration and Yt-HurKot assistance are accounted for?
It should be noted that chickens are capable of fighting diagonally, but only when in the Fight Cave. This little-known fact accounts for the fact that TzTok-Jad is actually allergic to chicken, even though the temperature in the TzHaar city is actually too high for any normal chicken to survive longer than a few minutes. For convenience, I assume roosters can do the same.
The Maths
First, some interesting numbers:
A rooster has 70 life points. They have a 0.77% chance of hitting TzTok-Jad, and then only a 50% chance of inflicting a measly 10 life points in damage. Against an Yt-HurKot they are much more successful, and have a 5.48% chance of hitting, followed by the same 50% chance of inflicting 10 life points of pain.
TzTok-Jad has 2500 life points, and will ordinarily regain 10 lost life points every minute. When he has 1500 life points left, four Yt-HurKot will spawn to heal him. As a godly creature of magma-fuelled destruction, TzTok-Jad has an average chance (across all attack methods) to hit a rooster of 99.78%, and has an average maximum hit of 965 damage.
Yt-HurKot have 600 life points, and will heal 10 life points per minute. They have a 98.85% chance of hitting a rooster, and can inflict up to 110 life points of damage.
Right, on with the amusing theories…
Each rooster has a 0.385% chance of wounding TzTok-Jad, so you need 259.74 roosters to inflict one hundred life points of damage. As TzTok-Jad has 2500 life points, it will therefore require 64,935 roosters to defeat TzTok-Jad in a single instant of frenzied pecking.
Because we can still assume that 64,935 pecks are required, and that 24 occur each attack cycle (which, for a rooster, is approximately every 2.4 seconds), we can know that it will take 6,493.5 seconds, or 1 hour 48 minutes 13.5 seconds. Not bad, for a pack of feathered wimps, I’m sure you’ll agree! The roosters, however, are constantly being attacked by TzTok-Jad, who has a 99.78% chance of hitting a rooster in melee, and a 92.75% chance of killing them outright with each hit, so he has a 92.55% chance of killing a rooster with every attack. In the time he survives, TzTok-Jad would be able to slay 2,509 roosters, so you would then only need 2,533 roosters (because you still need 24 roosters around Jad at the time of his demise).
Roosters are foolish creatures and unlikely to think of attacking the Yt-HurKot as they arrive to heal their master, so it would then become effectively impossible.
If, however, the roosters were elevated intellectually to the level at which this would occur to them, they could easily continue to attack TzTok-Jad while the remaining thousands of feathered beasts deal with the irritating little blighters. This will, of course, take much longer and require far more birds.
TzTok-Jad heals himself at a rate of 10 every minute, while the 24 roosters are inflicting ten points of damage every 25.97 seconds on average, so the roosters instead inflict 131 life points of damage every minute (TzTok-Jad having healed 100 life points during that time). This means that it will take them 1 hour 16 minutes 20.4 seconds to get TzTok-Jad to 1500 health, thus spawning the wretched Yt-HurKot, and a further 1 hour 54 minutes 30 seconds to finish him off if the other roosters are capable of occupying them. TzTok-Jad, therefore, will be able to slay 4,593.65 roosters in the 3 hours 10 minutes 50.4 seconds the battle lasts.
The Yt-HurKot, meanwhile, will no doubt be finishing a few off themselves. The chickens have a 2.74% chance of doing 10 points of damage to an Yt-HurKot every 2.4 seconds, but 8 can attack each of them, so will do 21 life points’ damage every time they attack. At this rate, it will take them 12 minutes 45.6 seconds to kill an Yt-HurKot (including the time calculated for the Yt-HurKot’s normal regeneration). In that time, however, their prey will finish off 172.43 roosters. As Yt-HurKot only respawn regularly if TzTok-Jad gets back to full health, the birds will only have to face 4 of them and suffer a loss of 689.72 of their number.
In total, this means that you will need 5,308 roosters to make it through the previous 63 waves in order to have good odds of winning a fire cape. Of course, roosters have no need of capes, so they’ll probably just ask for some TokKul so they can save up for an onyx to craft into a ring of stone, in the hope that at least one of their hens will survive the brutal culling they face every day at the hands of eager fletchers and adventurers completing Cook’s Assistant.
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