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Today is January 22, the 22nd day of the year 2024.

I chose today because 22 is my favorite number.

Now for the problem. Try to relate 22 to 2024 using math.

For example, 58 is related to 271 because 271 is the 58th prime number.

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2024 is…

the 22nd tetrahedral number. That is, $2024=\dfrac{22\cdot23\cdot24}6$.

What does this mean, though?

If you had a pyramid of spheres with a triangular base with side lengths of $22$, and stacked each one such that it was stable, there would be $2024$ spheres total. It's like those fruit pyramids one may or may not see at a supermarket. In addition, since $2024=\dbinom{24}3$, it actually appears on Pascal's Triangle! Neat!

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  • $\begingroup$ Nothing really, I just wanted to see if there were people who knew about it. $\endgroup$ Commented Jan 23 at 3:06
  • $\begingroup$ Nice. How did you find this? WolframAlpha? What's Special About This Number (erich-friedman.github.io/numbers.html)? $\endgroup$ Commented Jan 23 at 3:08
  • $\begingroup$ I just remembered that 2024 was a tetrahedral number and looked up 22*23*24/6 in the URL bar. Luck and pre-had knowledge. And the "What does this mean, though?" was just describing the meaning of a tetrahedral number. $\endgroup$
    – Someone
    Commented Jan 23 at 13:33

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