Arrr, me hearties! Avast ye! A blessed contraption, a 'puter, hath cracked the riddle o' the 'Packing Coloring'!
2023-07-02
Arr, ye be seekin' the answer to how many numerals be needed to fill an endless grid, with none o' them identical numbers drawn too near each other? Aye, me hearties! The answer be simpler than ye may reckon!
Arrr, me hearties! Gather 'round, for I have a tale to tell ye about a puzzling conundrum that would make even the fiercest pirate scratch his head. Picture this: a vast, infinite grid stretchin' far and wide, beggin' to be filled with numbers. But beware, me mateys, for we must place these numbers with caution, lest identical ones happen to be too close together!Now, ye might be wonderin': how many numbers must we gather to solve this perplexin' problem? Fear not, for the answer be surprisingly straightforward! Arrr, it be but a matter of logic. Ye see, if we consider each number as a ship sailin' on the high seas of our grid, we be needin' just a handful of ships to navigate this treacherous terrain.
Let me explain, ye landlubbers. Think of the first number as the captain of our fleet, bravely settin' sail into the vast unknown. Aye, this ship can claim any spot on the grid, for no other ship be out there yet! But as we add more numbers to the mix, things get a tad trickier.
We must be clever, me hearties, and give each new ship a spot on the grid that be a safe distance away from the others. But what be this mystical distance, ye ask? Well, it be a number called the golden ratio, but let's not get too caught up in that, shall we?
As our fleet of numbers grows, we find that each ship needs to be placed at a distance equal to the sum of all the previous ships' numbers. Aye, ye heard me right! It be a bit like a dance, with each ship carefully choosin' its partner to keep a safe distance away.
So, me hearties, to answer yer question: we need only a handful of these numbers to fill the infinite grid without any identical ones gettin' too cozy. And with a bit of mathematical know-how and a sprinkle of pirate humor, we can conquer this puzzle and sail the seas of numerical adventure!