7 Beautiful Patterns Behind The Unique Mathematical Year 2025! - YouTube
(20 + 25)2 = 45² = 2025
2025 is also divisible with sum of its digits
(2+0+2+5)² * 5² = 92 * 52= 81 * 25 = 2025
(1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9)² = 45² = 2025
13 + 23 + 33 + 43 + 53 + 63 + 73 + 83 + 93 = 2025
2025 is also sum of first 45 odd numbers
1 + 3 + 5 + ... 89 = 2025
and a sum of "multiplication table" 1-9 x 1-9
const { log: print } = console // JavaScript, to make compatible with Python syntax
print((20 + 25) ** 2)
> 2025
print(9 ** 2 * 5 ** 2)
> 2025
// # 2005 can be divided by sum its digits
print((2+0+2+5) ** 2 * 5 ** 2)
> 2025
// # 2005 is square of sum of first 9 numbers
print((1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9) ** 2)
> 2025
// # 2005 is sum of cubes of first 9 numbers
> 2025
// # 2005 is sum of first 45 odd numbers
let sum1 = 0
for(let i = 1, j = 1; i <= 45; i+=1, j+=2)
sum1 += j
print(sum1)
> 2025
// same, more compact, less readable, JavaScript
console.log([...Array(45)].reduce((sum, _, i) => sum + (i * 2 + 1), 0));// one line python code
print(sum(range(1, 90, 2)))
// # 2005 is sum of multiplication table of 1-9 * 1-9
let sum2 = 0
for(let i = 1; i <= 9; i++)
for(let j = 1; j <= 9; j++)
sum2 += i * j
print(sum2)
> 2025
// one-line python code
print(sum(i * j for i in range(1, 10) for j in range(1, 10)))
print(sum(i * j for i in range(1, 10) for j in range(1, 10)))
Also: 2025 =
"Number of ways you can hit 4 different numbers on a dart board with 2 being even and 2 being odd"
"Number of ways you can hit 4 different numbers on a dart board with 2 being even and 2 being odd"
Thansks Bill Mather!
E = total even numbers on dart board = 10
O = total odd numbers on dart board = 10
AI solution (both Google and ChatGPT)
The number of ways to choose 2 even numbers from is:
= 10 * 9 / 2 = 45The number of ways to choose 2 odd numbers from is:
= 10 * 9 / 2 = 45
Since we want 2 even numbers and 2 odd numbers, the total number of ways is:
45 * 45 = 2025
