HHC 2018 Programming Contests

[Gene]

I did not program this, but my thinking went this way... feel free to tell me where I went wrong. :-)

Approach 1:

I treated a triple positive or triple negative as a LCM problem. The 23 day cycle has a +100 or -100 on days 5.75 or17.25. The 28 day cycle on days 7 and 21. The 33 day cycle on days 8.25 and 24.75.

Assumption: The +100 has to be an exact match. A +100 day did not count if it was a 99.8 and a 100.2 and a 100. This could be wrong, but ...

Since you can't (easily?) do a LCM on a decimal number, I found the LCM of 575, 700 and 825. This value is 531,300. Dividing by 100 again, makes a triple event every 5313 days.

So birth plus 5313 should be a triple, plus another 5313 would be a triple, etc. If not, where did I not think properly?

Alternatively...

Approach 2:

I found a website :-) that would do Maximum and minimum bio-dates. This generated a period of 17003 days between extremums. This does not match approach 1, but ... ?

Thoughts?