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This puzzle is impressed by JLee’s What’s a Phrase/Phrase™ collection and the next “Quantity” variants. (Really, I would initially tried to create a extra unique puzzle utilizing the identical thought, but it surely became one other one in all these. Sigh. Possibly the kinds of numbers given lend this considerably extra novelty.)
If a constructive actual quantity obeys a particular rule, I name it a Good Pasta Quantity™. Listed here are some examples:
| A very good, strong pasta! Yeah! | You’re a horrible cook dinner |
|---|---|
| $6sqrt{6}$ | $3sqrt{5}$ |
| $6$ | $8$ |
| $3sqrt{6}$ | $6sqrt{3}$ |
| $frac{3sqrt{2}+sqrt{6}}{2}$ | $frac{3sqrt{6}+sqrt{2}}{2}$ |
| $3sqrt{50-22sqrt{5}}$ | $3sqrt{50+22sqrt{5}}$ |
| $9sqrt{3}-3sqrt{15}$ | $18sqrt{3}-6sqrt{15}$ |
| $frac{42sqrt{6}}{23}$ | $frac{56sqrt{6}}{19}$ |
| $frac{15sqrt{6}-18sqrt{3}+135sqrt{2}-162}{14}$ | $frac{15sqrt{30}-18sqrt{15}+135sqrt{10}+30sqrt{6}-162sqrt{5}-36sqrt{3}+270sqrt{2}-384}{14}$ |
There are a lot of extra Good Pasta Numbers™ not proven above, however solely a finite quantity.
Which numbers make an excellent pasta™?
Be aware:
There’s nothing hidden within the flavortext apart from a really refined connection (probably not a clue); this actually is only a regular “What’s a _______” puzzle. I like making my puzzles enjoyable to learn. Additionally, the property is restricted to the numbers themselves, and never any particular illustration of the aforementioned numbers.
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