I've been mentoring students and professionals for over a decade.
Based on this experience, I've created an (almost) exhaustive list of the most impactful rules & concepts.
Make 2024 your best year: π
Irony: social media influencers mocking a kid with dreams.
Not even an original mocking, copied from elsewhereπ
Only someone with an "aim", has the possibility to achieve it. So, probably he or someone like him.
For anyone trying to pull him down, why not first reply with the IIT you graduated from.
@Labgo@pickover One region was lost due to symmetry.
If you move any one point on circle slightly, you'll find 1 more region emerge in the center.
Hence, resulting in 31 regions.
@pickover It would be 31 β
The series that forms is:
1, 2, 4, 8, 16, 31, 57, 99, 163, 256, ...
It can be derived using βΏCβ + βΏCβ + 1 βοΈ
If wondering why it appeared like 2βΏ for initial terms, the answer lies in the Pascal's triangle:
https://t.co/nplZqq54w2
The coefficients are the numbers in Pascal's triangle (which is extremely easy to create). In any row, just add the two adjacent values and it gives the value below.
This allows to skip the tedious calculation and find next expansion just by using the current one.
@pickover@gs_bangalore There are 9 rows and 9 columns, so total rectangles
= Ξ£9 * Ξ£9
= 45 * 45
= 2025 β
Explanation:
Out of 9 rectangles in rows (or columns), "k" continuous rectangles can be selected in "10-k" ways (k β [1,9]).
Hence, resulting in 1+2+...+9 = Ξ£9 ways to select from rows/cols.
@horsemankukka Right, glad that you mentioned.
Initially, I wrote "such year had never occurred for 4 digit years", then while rephrasing/editing seem to have missed that part.
Happy New Year, 2025 ! π₯³πβ¨
May this year bring you joy, prosperity and everything you wish for !
Numerically, year 2025 holds rare gems which won't occur for decades and centuries. Let's explore π§΅π