Pickover’s puzzle for the weekend of February 4-5 challenged the reader to find 8 numbers to stand in for the letters D, E, G, M, N, O, R, and S such that the equation SEND + MORE = GEESE would be true. Again, there are multiple solutions. I’m pleased to report that I found 3 orders of magnitude more solutions than the big brain himself.
At first I tried to set up a series of equations. It’s obvious from the right side of each number that D must be 0 (D + E = E; D = E – E; D = 0). But beyond that, anything’s possible. So I eventually went to code. Pickover claims to have worked through 6 unique solutions. I figured that’s all there are. However, when I let my program rip I found precisely 1000 solutions. Caveat: The original problem statement never said anything about each of the 8 digits needing to be unique. Thus, for example, if all 8 variables are 0, that would be a valid solution. If someone wants to haul out the permutation logic and make sure that all the digits being tested are unique, it would be interesting to see if there are more than 6 solutions.
Here’s my code:
/*
* Program to brute-force the solution(s) to Cliff Pickover's
* 2006/02/04 puzzle.
*/
#include <stdio.h>
int main(void)
{
int d, e, g, m, n, o, r, s;
int send, more, geese;
int count = 0;
for (d = 0; d < 10; d++)
for (e = 0; e < 10; e++)
for (g = 0; g < 10; g++)
for (m = 0; m < 10; m++)
for (n = 0; n < 10; n++)
for (o = 0; o < 10; o++)
for (r = 0; r < 10; r++)
for (s = 0; s < 10; s++) {
send = s * 1000 + e * 100 + n * 10 + d;
more = m * 1000 + o * 100 + r * 10 + e;
geese = g * 10000 + e * 1000 + e * 100 + s * 10 + e;
if (send + more == geese)
printf("solution %d: %d + %d = %d\n", ++count, send, more, geese);
}
return 0;
}
It requires ~37.4 seconds to run on my 512 MHz, x86-based CPU. For the optimization-obsessive personalities among our ranks, I replaced all of the multiplications with table lookups. That brings the nominal runtime down to 17.8 seconds.
/*
* Program to brute-force the solution(s) to Cliff Pickover's
* 2006/02/04 puzzle.
*/
#include <stdio.h>
int main(void)
{
int d, e, g, m, n, o, r, s;
int send, more, geese;
int count = 0;
int tens[10];
int hundreds[10];
int thousands[10];
int tenthousands[10];
for (d = 0; d < 10; d++) {
tens[d] = d * 10;
hundreds[d] = d * 100;
thousands[d] = d * 1000;
tenthousands[d] = d * 10000;
}
for (d = 0; d < 10; d++)
for (e = 0; e < 10; e++)
for (g = 0; g < 10; g++)
for (m = 0; m < 10; m++)
for (n = 0; n < 10; n++)
for (o = 0; o < 10; o++)
for (r = 0; r < 10; r++)
for (s = 0; s < 10; s++) {
send = thousands[s] + hundreds[e] + tens[n] + d;
more = thousands[m] + hundreds[o] + tens[r] + e;
geese = tenthousands[g] + thousands[e] + hundreds[e] + tens[s] + e;
if (send + more == geese)
printf("solution %d: %d + %d = %d\n", ++count, send, more, geese);
}
return 0;
}
C code colorized by the CodeColorizer.
Hi Mulitmedia Mike.
I am a fan of Clifford Pickover. Pickover introduced me to the topics of Bertrand Russell’s twenty favorite words, the Saphir-Whorf Hypothesis, French theater critic Georges Polti, Ernest Wright’s “Gadsbyâ€, the Racter program, the Barcelona based Polyphonic HMI, his book Dreaming the future etc. I have two of his books and would glady read more. Perhaps you or your audience could use a search engine to explore the topics just mentioned if you are unfamiliar with them.
Hurray for Clifford Pickover, the Hilbert cyber space in the times of the 21st century man.
About me, I worked for a marketing firm that specialized in Pay Per Click Search Engine Campaign management as a de facto copywriter negotiating trial of service contracts as a business developer and I’ve moved on. My question involves a ‘basin of attraction’ for these ‘geese’ with herring (perhaps red, maybe blue, a Ramsey number or in general perhaps less literal and more figurative).
About the topic of reverse engineering technology in multimedia, as musical group Talking Head’s David Byrne would say, ‘well… how did I get here?’ Hint: search engine que on ‘pickover’ on a wild goose chase of the relationship between keyword management and inovative copywriting techniques, plus topics of another excelent author of literary works, Manfred Schroeder in the parameters of SEM (search engine marketing).
In Manfred Schroeder’s explination of Newton’s tangent method in the complex plane, “the line in the complex number plane for which the real part of z subset 0 vanishes (i.e., the imaginary axis) is the boundary plane between the two basins of attraction of the two solutions +1 and -1, repectively. Easy as pie.” from pg. 39 of his book (more later).
May I also suggest Paul Nahin’s ‘Imaginary Tale’ as well, Pickover sure has already. From Nahin’s book: “1.2 Negative attitudes about negative numbers …John Wallis (1616-1703) makes the argument since a / 0, with a > 0, is positive infinity, and since a / b, with b
So again search enginge enigma of Teilhard de Chardin type terms as ‘noosphere’, how did I get here? Sum of a limit, Leibneiz ‘n his monads! Yes, yes this wild goose chase of Pickover puzzles in the engines of ingenuity search.
In the parameters of Keyword analysis for PPC (Pay Per Click) SE (Search Engine)Marketing Management relevant for ad-copy and copywriting development, free resources are available from
Overture:
http://www.inventory.overture.com
http://uv.bidtool.overture.com/d/search/tools/bidtool/
Using Microsoft Excel Spreadsheets, the PPCSE Keyword(s) may be analyzed within a landscape of marketers and consumers. This vehicle being suggested is how to find out what various online marketers PPCSE campaign are and the relationship it(or they) has with competing marketers (Bid wars are problematic). Software (Excel?) and innovations are currently in development such as MIT (Massachusetts Institute of Technology) project of “Hypersuit†, developments at IIT (Indian Institute of Technology) in the Academic sector as well as a cornucopia of services and products offered in the private sector.
The Google Search Engine has a more selective information system design for PPCSE marketing services they offer:
http://www.google.com/analytics
https://adwords.google.com/select/KeywordToolExternal
It is free to utilize the Google service of analytics for PPCSE analysis however the information is more selective than that offered by Overture.
Analyzing KW (keywords) reveals popularity from the internet masses within search engine media parameters. This is valuable information that may be applied in the field of technical communication: ad-copy and copywriting development, brochure copy, content of web pages, etc. I also recommend the free resources offered to the online copywriter from Nick Usborne at:
http://www.excessvoice.com/
and also Copywriter Bob Bly:
http://www.bly.com/
Oh and by the way, yes Pickover offers a wealth of resources for the St. Francis patron saint of Journalist beatific audience as such an attentive and entertained sort as any reading thus far of this subject matter.
What I’d really like to know multimedia Mike, is if the actual monkeys that Mandelbrot utilized in his experiment to debunk Zipf went on to write an exact word for word copy of one of Shakespeare’s work with some other mathematician or physicist (dirty be-itch’s). Perhaps it was the monkeys kids or grandkids that explains Primate Programing Inc.:
http://www.newtechusa.com/ppi/main.asp
In theory, I stand by my claim that one may attract more geese with herring. Curses, ney, cursed cursing of curses to theory (Recursive?, poor Turning, sad as Hausdorf or Lovelace). As Falcon Press authors have suggested, follow the cheese to the maze. You know, that Thorndike was a real Skinner said the souless shrink and/or how does Julian B. Rotter’s concept of locus of control and predictive formula fit in to this search engine equation?
A fan
Back to Manfred Schroeder and the critical relevance to this post here, Manfred goes on to suggests “…one of the more surprising instances of a power law in the humanities is Zipf’s Law connecting word rank and word frequency for many natural languages… Claude Shannon, the creator of information theory, has used Zipf’s law to calculate the entropy of a source of English text that sputters words independently with Zipf’s probabilities… George Zipf endeavored to derive his law from Human Behavior and the Principle of Least Effort (the title of his 1949 treatise). But Benoit Mandelbrot, in an early effort, has shown that a monkey hitting typewriter keys at random will also produce a “language†obeying Zipf’s hyperbolic Law.â€
*didn’t copy and paste properly*
From Nahin’s book: “1.2 Negative attitudes about negative numbers …John Wallis (1616-1703) makes the argument since a / 0, with a > 0, is positive infinity, and since a / b, with b
Must be an HTML read error, …
Ack, a math concept being literally explained!
…
This left Wallis with the astounding conclusion that a negative number is simultaneously both less than zero and greater than positive infinity.
*didn’t copy and paste properly*