Abhishek Verma π»
@intelocode
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Coding for 15+ years | Sr. Software Engineer | IIT Kanpur alumnus | CP: 99.5+ %ile | Tweets: Computer Science, Maths & Psychology | Expertise: Problem Solving
Sweden
Joined January 2021
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
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An interesting way to check if the given alphabet is vowel using bit manipulation. Have a look if you understand how it works !
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That's the end of thread ! π I post about Problem Solving, Computer Science, Mathematics & Psychology. If you enjoyed the thread, consider following (@intelocode) for more such content. Thank you ! π
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Bonus fact if you're interested in primes: 2025 + 2 is a prime number β2025 + 2 is a prime number 2025Β² + 2 is a prime number
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Btw, the word "harshad" comes from Sanskrit, harsh (joy) + da (give) meaning joy-giver. So, I hope current quadrennium of harshad years 2022-2025 fills your life with joy. This is the last year of the quadrennium and also has an immaculate factorized form: 2025 = 3β΄ * 5Β²
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Also, I discovered a fascinating phenomenon for the current years (2022-2025), they're Harshad years. To begin, Harshad number is a number divisible by sum of its digits. E.g. 2023 is divisible by 2+0+2+3 ie 7. But this phenomenon (2+ consecutive Harshad years) is so rare that
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Trigonometrically, tangent of 2025Β° is 1. Obviously, happens 180 years apart. And since, 2025 = 27Β² + 36Β² Hence, 2025 can be represented as hypotenuse of a right triangle with integral sides. Last such year was 1681 ( = 9Β² + 40Β²), Next such year will be 2809 ( = 28Β² + 45Β²).
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2025 is a centered octagonal number. Such numbers are represent an octagon with a dot in the center with surrounding dots in successive octagonal layers. Last such year was 1849, Next such year will be 2209.
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As per Nicomachus' theorem: 1Β³ + 2Β³ + ... + nΒ³ = (1 + 2 + ... + n)Β² Hence, the previous fact can also be stated as 2025 being square of a triangular number. 2025 = (1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9)Β²
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2025 is also a Cube Year. 2025 = 1Β³ + 2Β³ + 3Β³ + 4Β³ + 5Β³ + 6Β³ + 7Β³ + 8Β³ + 9Β³ = Ξ£ iΒ³ Last such year was 1296, Next such year will be 3025.
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2025 is a perfect square ie 45Β² Last such year was 1936. Next such year will be 2116. In fact, 2025 can be broken in two parts to express as 2025 = (20 + 25)Β² Such year had NEVER occurred, Next such year will be 3025.
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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
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Received "1000 Days Badge" on @LeetCode today. Frankly, I've been solving just the daily-problems mostly. And it lead to 1000+ problems & 50+ badges. If you've similar goal, a few minutes everyday will easily take you there. Just start and be consistent ! π
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Mathematics and beauty. Here's an eye-catching equation connecting i, e and pi. The left-hand side has only imaginary terms, and the right-hand side has only real terms. Source: https://t.co/x3FVfR1sqX
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Those are midnight clicks ! June Solstice turned midnight into an evening.
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It's Monday: time to practice problem solvingβ‘οΈ This puzzle comes from Game theory and involves both logic & human behavior. πΉ There are 'k' kids in a family and a cake needs to divided & distributed among them πΉ Kids are likely to be dissatisfied with their share What
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When Einstein said "Imagination is more important than knowledge" he didn't mean that your "imagined parachute" will save you if you jump off the aircraft ! π€¦ββοΈ
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What I love about mathematics is that a simple idea can be extended to unexpected limits and it may still work perfectly. Moreover, it often leads to further insights ! For instance, as number of sides in regular polygon are increased, it approaches circle. This simple idea can
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I am surprised to see amount of calculations in comment section. Such problems are much easier with shifting. Shift top triangle to the bottom and right-side triangle to the left. Then the yellow area perfectly fits within 3x4 rectangle. Hence answer is 12. β
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What I love about mathematics is that a simple idea can be extended to unexpected limits and it may still work perfectly. Moreover, it often leads to further insights ! For instance, as number of sides in regular polygon are increased, it approaches circle. This simple idea can
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