# Enigmatic Letters

I call them Recurro, Terminato or Perfecto if the letters conform to my conditions.

Recurro:A, B, G, H, K, N, Y, Z

Terminato:E, M, Q, W

Perfecto:C, D, F, I, J, L, O, P, R, S, T, U, V, X

Find the conditions.

Clue: Corresponding lowercase letters are not necessarily in the same category.

• If you combine all the letters it forms the incantation to summon Cthulhu. – John Clifford Aug 9 '17 at 8:52
• I thought I had a partial solution for Recurro, but G doesn't seem to fit it. I was thinking that every letter has two equal segments and one different segment, but G doesn't follow that convention. Oh well. – David Foong Aug 9 '17 at 12:56
• Actually David I think you're onto something. The equal segments would be the lines going up and left from the bottom of the curve. – John Clifford Aug 9 '17 at 17:38
• Almost wanted to say Perfecto letters are symmetrical, but there are too many symmetrical letters that don’t fit and too many asymmetrical letters that do. – DonielF Aug 9 '17 at 17:58

Well, I have a logic

The number of strokes required to write Recurro type letters is 3 and inverse of 3 is recurring

For others,

Terminato type letters, 4 strokes are needed and inverse of 4 is terminating (need to check for Q, if it can be written differently)

And

For Perfecto type letters either 1 or 2 strokes are enough and inverse of 1 or 2 is obvious.

Based on

Tom's inputs, here is a complete solution: Get the index of an alphabet, starting with A=1, proceeding futher like B=2,....till Z=26

and

Get the number of 'different' strokes / line segments needed to write a letter in capital. Now divide the index by the number of strokes to get like For 'A' : index = 1, strokes = 3 and thereby giving a fraction 1/3, which is recurring...(similarly others can be tested B with 2/3, G with 7/3 etc. - giving 'Recurro' type letters For E, they are 5 and 4(5/4), M - 13 and 4 (13/4)..which terminate and thereby Terminato and For C they are 3 and 1 (3/1), D - 4 and 2 (4/2) ... which end us with proper integers like 3,2, and so on and hence are 'Perfecto'.

• How do you define “strokes”? I can write a B with just one stroke. – DonielF Aug 9 '17 at 17:57
• Wow, I actually thought about counting strokes, but I didn't consider taking the inverse. In addition, F and I (potentially R as well) take three strokes. Other than that, I like this answer – David Foong Aug 9 '17 at 17:58
• And what is the difference between perfecto and terminato if you accept two-stroke characters? 1/4 = .25 and 1/2 = .5. Those are both terminating. Q doesn't really work either. – David Foong Aug 9 '17 at 18:06
• @MeaCulpaNay, like A = 1/3 = 0.33.. & B = 2/3 = 0.66.. (recurring) , C = 3/1 = 3 & D = 4/2 = 2 (perfecto/whole), E = 5/4 = 1.25 (terminating). You could call your strokes - smooth differentiable segments. – Tom Aug 10 '17 at 9:03
• @MeaCulpaNay No problem, just following-up your solution, and you could add this A1-Z26 numerator and 'number of strokes' denominator to your answer. A lower case letter like b would have two strokes. (I only used Rot13 to hide my first comment.) – Tom Aug 10 '17 at 10:21