Well the root of 2024 is greater than 42, so it's probably a trick question with no real answer. 

Aardvark

I figure this would be a fun one to try and code in one line :)

`np.sum(np.floor(np.sqrt(np.arange(1,2025,1))))`

Answer: `59730`

SimpleStacker

If we write down the floor values we see
$$
S = 1 + 1 + 1 + 2 + 2 + 2 + 2 + 2 + 3 + 3 + 3 + 3 + 3 + 3 + 3 + 4 + ... + 44
$$
(note how, conveniently, $$\sqrt{2024}$$ is just at the border between 44 and 45)
or
$$
S = \sum_{k=1}^{44}{k \times (2k + 1)}
$$
or
$$
S = 2 \times \sum_{k=1}^{44}{k^2} + \sum_{k=1}^{44}{k}
$$
and then using the Sums of powers formula from the suggested page
$$
S = 2 \times \frac{44^3}{3} + \frac{44^2}{2} + \frac{44}{6} + \frac{44*45}{2} = 59730
$$


Scroogey

[Empirically](https://glot.io/snippets/h1m2xvq4bq) $$S=59730$$.

science

What does this sum S equal to?

$$
S = \lfloor \sqrt{1} \rfloor + \lfloor \sqrt{2} \rfloor + \lfloor \sqrt{3} \rfloor + ... + \lfloor \sqrt{2024} \rfloor
$$

Note that $$\lfloor x \rfloor$$ refers to the floor value of $$x$$, _i.e._ $$\lfloor pi \rfloor = 3$$

[This page](https://en.wikipedia.org/wiki/List_of_mathematical_series) might be useful at some point if you encounter a sum of powers.

Previous iteration: https://stacker.news/items/758044/r/south_korea_ln (several correct answers where indeed, prisoner 2 is the one that speaks, naming the opposite color to the one in front of him).