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I wrote this puzzle last year, but didn't post it in time, so I've re-written it for this year. Here's an elegant function f with range and domain as subsets of the natural numbers, some of which values are given to you:

  • f(1)=100
  • f(2)=50
  • f(4)=25
  • f(5)=20
  • f(10)=10
  • f(100)=40
  • f(106)=25
  • f(110)=20
  • f(115)=16
  • f(125)=100
  • f(201)=35
  • f(209)=25
  • f(350)=75
  • f(354)=60
  • f(358)=50

Solve for f(x)=48.

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    $\begingroup$ An arbitrary number of functions can pass through a given finite set of data points. $\endgroup$ Commented 2 days ago
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    $\begingroup$ @vallev Hence why I add the modifier "elegant". For instance, it wouldn't be fair to call a Right-wing Word™ "any word that is either ARM, BUMP, SECT, CHILL, ACT, CRIMP, SWIM, DRILL, KILL, ASSERT, SERUM, or JUMP". $\endgroup$ Commented 2 days ago

1 Answer 1

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You have good taste in puzzle gimmicks, because this is similar to one I've stewed on before.
f(n) is the function that

takes the n'th day of the year, and converts its date, as a fraction MM/DD, to a percentage!
The dates in order are 1/1, 1/2, 1/4, 1/5, 1/10, 4/10, 4/16, 4/20, 4/25, 7/20, 7/28, 12/16, 12/20, and 12/24.

f(359)=48, corresponding to 12/25, Christmas!

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    $\begingroup$ Correct and intended, well done! Thank you for your complement. Perhaps you can explain the flavor text as well? $\endgroup$ Commented 2 days ago
  • $\begingroup$ Didn't realize that was intended as a hint, but you reveal spoiler had to rewrite the puzzle because last year was a leap year. $\endgroup$ Commented 2 days ago
  • $\begingroup$ Correct and intended. $\endgroup$ Commented 2 days ago

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