2023-8: Critical Thinking
The biorhythm theory is a pseudo-scientific idea that one's life is affected by three rhythmic cycles beginning from one's date of birth. The cycles are:
- The Physical cycle, with a periodicity of 23 days, affecting co-ordination, strength, and general well-being
- The Emotional cycle, with a periodicity of 28 days, affecting creativity, sensitivity, mood, perception, and awareness
- The Intellectual cycle, with a periodicity of 33 days, affecting alertness, analytical functioning, logical analysis, memory, and communication
"Critical days" are days when a cycle crosses the x-axis in either direction and are purported to be accompanied by unstable conditions in the corresponding area. A "double critical day" occurs when two of the three cycles cross the x-axis on the same day. Starting from one's birthdate, double critical days occur on multiples of the least common multiple of the half of the periodicities of the two involved cycles. Thus Physical-Emotional, Physical-Intellectual and Emotional-Intellectual double critical days can be calculated respectively using multiples of:
23 23 28∧⍥(÷∘2)28 33 33
322 379.5 462
Fortunately, the dreaded "triple critical day", when all three cycles cross the x-axis on the same day, only occurs every (∧/23 28 33÷2) or 10,626 days (a bit more than 29 years).
Write a function that:
- takes a 3-element integer left argument representing a valid birthdate
- takes a 3-element integer right argument representing a valid date occurring on or after the left argument
- returns a 3-element integer array representing the date of the next double or triple critical day occurring on or after the date represented by the right argument.
Note: All the dates in this specification are to be in the form year month day
Hint: The date time system function ⎕DT and residue function | could be helpful in solving this problem.
Examples:
1962 10 31 (your_function) 2023 1 1
2023 2 4
1961 2 23 (your_function) 1961 2 23 ⍝ one's birthdate is a triple critical day
1961 2 23
your_function ←
Solutions
