Re: A Problem To Solve :-)

On 3/31/24 19:40, Physfitfreak wrote:

  If the missile computes that 5 fighter jets at time t will exactly be at these coordinates in the sky:
 Jet 1: (4.38 km, 3.9 km, 8.1 km)
Jet 2: (5.23 km, 9.61 km, 4.74 km)
Jet 3: (6.93 km, 6.01 km, 6.88 km)
Jet 4: (8.32 km, 2.12 km, 2.5 km)
Jet 5: (2.53 km, 4.23 km, 5.82 km)
 then answer the following 2 questions:
 1- what would be the coordinates of the point in the sky, that the missile with the weakest warhead needs to explode at, at time t, to damage all those 5 fighter jets critically enough?
 2- within what maximum radius of that explosion, any fighter jet would get critically damaged at time t?
       

It took Physfit just half hour to solve as well as code the problem, then Houthis updated their Missile's software to use that subroutine to aim at a point other than directly where any fighter jet would be. This worked pretty well for them, and after the Nazis lost a few fighter jets too many, they backed off like Bill Gates had backed off from the scenery down the Mossberg barrel,
Nazis:   "Those Houthis now hit us five at a time??... FUCK _ME_!"
After Nazis were gone, Physfit looked around to study the place a bit better and perhaps even find a healthy restaurant of some sort nearby to eat at. He was still very hungry and did not remember when it was he last ate. So he could push it a little bit and assume that at least 48 hours had passed since.
Then while looking out the window,,, what do you know... he saw a Long John Silvers right there across the street!...
"Long John Silvers in Yemen?" he asked the same Houthi he'd talked before.
Houthi:   "Fish is Halal meat as you know, The franchise owner is a Houthi himself. We beheaded the earlier Nazi owner of the store. No infidels there now. So we often dine there."
Physfit:   "Good job! Is there anything strange about their menu prices?"
Houthi:    "Strange? No. The prices are reasonable."
So Physfit decided to go for a three fish fillet with huge coleslaw treat. He left the well camouflaged compound and entered the open space where he met the type of Sun one gets in Yemen for the first time in his life. It beat the Texas Sun something like 5-fold. But he still pretty well remembered the technique he and his elder brother had discovered to deal with Sun's punishments like that under Tehran's hottest days' Sun*.
Se he put that experience into use and it worked. All he needed to do was to reduce the stress all over the body as he walked rather slowly, especially paying attention to muscles around the eye and the eyelids. To adjust the light, without forcing it one bit, he allowed the eyelids to come down just enough to let the right amount of light inside the eyes, and carefully making sure no muscle around the eyes were flexed in any way to keep the eyelid just there.
In that way he crossed the distance from the compound to the store without even sweating. Mighty trick they'd found, he and his brother, in that hot day in north Tehran, early in 1970s.
Inside store was cool and comfortable. He went closer to the order area to take a look to see if they had a similar order of three fish fillets with a huge side of coleslaw, as in the nearest store in Dallas.
Physfit:   "Ahh Holy Crap. Not again..."
Prices were expressed not only in base e instead of 10, they were also presented in nested radicals!... some finite, and some even with infinite nested radicals. He searched and found the three fish fillets with a huge side of coleslaw and ordered it. The Houthi cashier asked in Arabic for some amount of Yemeni Rials.
"He must think I'm Arab", Physfit thought.
Not knowing the Arabic language, he looked at the price on the register machine but found that also expressed in nested radicals, so he just produced his wallet and took all the bills out and strangely enough found them in Rials. He handed all the bills to the cashier. Cashier took what he needed and gave the rest, together with the receipt, back.
The price on the receipt looked like this: (in base e)
       _____________________________________
      ╱         ____________________________
     ╱         ╱        ____________________
    ╱         ╱        ╱       _____________
   ╱         ╱        ╱       ╱      _______
╲╱    2 + ╲╱   2 + ╲╱  2 + ╲╱ 2 + ╲╱2 + ...
While waiting for the order to get ready, he decided to calculate that number. Soon order was ready and he had found the price as well, in base e. Price looked rather reasonable although he didn't know the conversion rate of Rial to Dollar.
He enjoyed his meal tremendously, then stood up and walked outside in the Sun, and began going back to the compound. The damn meal tasted even better than the ones in Dallas.
What was the price in base 10 in Dollars?