Play with the year

Happy happy 2026!

2026 is a happy number! By repeatedly summing the squares of its digits, we eventually reach 1: 2²+0²+2²+6² = 44 ⇒ 4²+4² = 32 ⇒ 3²+2² = 13 ⇒ 1²+3² = 10 ⇒ 1²+0² = 1 ⇒ It's a happy year. If a number doesn't reach 1, it is called an unhappy number. Can you find any others?
2026 is also a semiprime number: 2026 = 2 · 1013 and the sum of two squares: 2026 = 45² + 1²
October, the 24th of this year (10/24/26) will be a pythagorean day, because
10²+24²=26²
Finally, on August 12th, there will be a total solar eclipse visible across most of the country, especially in the north.

Playing with the year

Rules:

Try to obtain every number from 1 to 100 using the digits of the new year: 2, 0, 2, 6.
On your turn, call out a number and explain the operation used to reach it. For example: 10 = 2+0+2+6
Each digit must be used exactly once.
You may use any mathematical operation at your disposal (addition, square roots, factorials, etc.).
You earn a positive mark for every new number. However, if you find a solution for a number already claimed, but yours uses the digits in their natural order (2, 0, 2, 6), you "steal" the point from your classmate.

Happy 2025!

2025 is a great number for Maths:

It’s a square (45²), the sum of two squares (27² + 36²), the product of two squares (9² × 5²), and the sum of three squares (40² + 20² + 5²).
It’s the sum of the cubes of the first nine positive integers (1³ + 2³ + 3³ + 4³ + 5³ + 6³ + 7³ + 83 + 93).
Equivalently, it’s the square of the sum of those integers (1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9)². (This is Nicomacus' Theorem).
It’s one of only three four-digit numbers whose halves can be split, summed, and squared to produce the original number: (20 + 25)² = 2025.
It’s the sum of the entries in a 9×9 multiplication table.
July 24, 7/24/25, will be a “Pythagorean day,” because 7² + 24² = 25².
When asked his age, Augustus De Morgan used to say, “I was x years of age in the year x².” (He was 43 in 1849.) People born in 1980 will be able to make the same cryptic response starting next year.

Source: Futility closet.

Happy 2024!

Did you know that in a meeting of 24 people you can make 2024 different groups of 3 people? Also, 2024 is a tetrahedral number.

Happy 2021!

2021 = 43 * 47, 43 and 47 are consecutive primes and also cousin primes (47-43=4). Nobody knows if there are an infinite set of cousin primes. Is there anything else special about this number?

Happy 2020!

¿Cuál es más grande, 2019^2020 o 2020^2019?

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