I love this number.
Find the sum of all the odd numbers between 10 and 550 that are divisible by three. Answered July 28 by Mike Alexander Studied ALevel Mathematics, Physics & Computer Science So, the odd numbers in the range go: [he shortens lists for visual reasons] 11 13 15 17 19 21 23 25 27 … 543 545 547 549 Every third number in bold is divisible by 3. [Remember the math fact: if the sum of the digits in the number equals three, the number is divisible by three. Try it with each one of the boldface numbers.] So, the sum is 15+21+27+33 … +543+549 Since all terms are divisible by 3, we can write this as: 3(5+7+9+11 … +181+183) [Because multiplication is the inverse of division. Proof: multiply the last number, 183, by three, and the product is 549.] Now notice that the series inside the parentheses is almost a full set of consecutive odd numbers  it just lacks 1+3+ at the start. So, it will be 4 less than the series: I will stop here. If you want the rest of the proof, click https://www.quora.com/HowdoIdothisarithmeticquestionFindthesumofalltheoddnumbersbetween10and550thataredivisibleby3 The final answer is 25,380. Guess what? The answer is divisible by three.
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