Problems & Puzzles: Puzzles
Puzzle 33.- Find numbers like this: 15551= Fifteen Thousand Five Hundred Fifty One = 383
(Proposed by G.L. Honaker, Jr. to me and to Patrick De Geest at , 9/12/98)
In the original proposal of this puzzle Honaker was asking for a scheme of the following type:
N à E(N), English expression of N à V(E), value of E
Very soon Patrick obtained "the number of the beast" from a palprime:
1215121 (palprime) = One Million Two Hundred Fifteen Thousand One Hundred Twenty One = 666. (P. De Geest)
and a second example of the like found by Honaker:
1496941 = O+N+E+M+I+L+L+I+O+N+ F+O+U+R+H+U+N+D+R+E+D+N+I+N+E+T+Y+S+I+X+ T+H+O+U+S+A+N+D+ N+I+N+E+H+U+N+D+R+E+D+F+O+R+T+Y+O+N+E = 727 = palindromic prime (Patrick De Geest)
Then I simply made my own search in Spanish (a=1, ñ=15, z=27):
1380831 (pal not prime) = un millón trescientos ochenta mil ochocientos treinta y uno = 666 (C. Rivera)
106909601(palprime) = ciento seis millones novecientos nueve mil seiscientos uno = 666(C. Rivera)
1936391 (palprime) =un millón novecientos treinta y seis mil trescientos noventa y uno = 787(palprime) (C. Rivera)
Maybe you would like to find other primes and/or palprimes in English; or maybe you would like to puzzle this way in your own language.
As for sure you have imagined, the very core of this puzzle is to develop your own code to make "easy" the step N à E(N). Do it youll enjoy
(On request you can ask by e-mail for the following codes available at this moment: NUMESP.ub, by Carlos Rivera and HONAPUZZ.ub by Patrick De Geest)
As a continuation of this puzzle, yesterday (Saturday, 12/12/98) I proposed to cycle the scheme designed by Honaker to an arbitrary starting number just to see where ends the game By example, In English I constructed the following sequence:
123456789, 964, 273, 298, 268, 278, 291, 253, 254, 258, 247, 281(prime), 240, 216, 228, 288, 255, 240 (a loop!)
Then I asked to Honaker, Patrick and Mike Keith (we were in touch that Saturday in an informal meeting by e-mails ) if every number always falls in a loop in every language.
The question did not last long in the air. Mike almost immediately answered this:
"This problem is discussed in Eckler's recent book "Making the Alphabet Dance." He cites a paper by Borgmann from 1967 that shows that every number in English converges to the 216-...-240 loop given by Carlos. Every number requires at most 18 steps to enter the cycle: an example of this is "4".
Isn't the following a remarkable fact? Every number in English converges to a single loop?!!!
Evidently I started trying to detect the loops available in Spanish and I found that same morning - without a very exhaustive search only three (3) loops:
1) 196, 242, 286, 196...
2) 222, 249, 309, 222...
3) 251, 298, 291, 300, 251...
Well, now the following questions appear interesting:
Q1)Can you verify that in English there exists only one loop (as Borgmann says)?
Q2)Can you see if in Spanish are there other loops besides the 3 found by Carlos Rivera.
Q3)Would you like to find the loops formed in other languages (come in friends of France, Belgium, Korea, Poland, and other countries!)
Claudio Meller wrote (May 2011!!!)
Jan van Delden wrote (May, 2011)