If $\lfloor x \rfloor$ is the greatest integer less than or equal to $x$, what is the value of $\lfloor \sqrt{1}\rfloor + \lfloor \sqrt{2}\rfloor + \lfloor \sqrt{3}\rfloor + \cdots + \lfloor \sqrt{49}\rfloor + \lfloor \sqrt{50}\rfloor$?

Same here lol. Once you see the pattern, it goes way faster.

Took me a second to spot it too. Grouping by perfect squares is the key.

Think about when the floor changes: it jumps at perfect squares.

For each integer k, count how many n have floor(sqrt(n)) = k. That's the gap between consecutive squares.

Nice, I got the same. The block from 36 to 49 caught me off guard for a second though.

Yeah, 217 felt right. The trap answers are pretty close so you have to be careful with the counting.

There's a general pattern: sum of k*( (k+1)^2 - k^2 ) over the relevant k range. But honestly, counting blocks is fast enough here.

For 50 terms, block counting is probably quicker than deriving anything fancy.