Sigma Test


What do prominent intellectuals say about the Sigma Test?

“Gosto imenso do Sigma Teste porque considero que em muitas questões precisa-se tanto inteligência como imaginação para resolvê-las.”  
Comment sent by Petri Widsten, from Finland, is Regent of Unicorn High IQ Society (IQ>180), member of Sigma Society VI (IQ above 196), Pi Society (IQ>176), ISI-S (IQ>151), Glia Society (IQ>150) and Mensa-Finland (IQ>132). Petri is holder
a Ph.D. Summa Cum Laude in Chemistry (Helsinki University of Technology) and win the prize 2003-2004 of the best Ph.D. thesis in Finland. He speaks fluently 9 languages, 2nd. Highest Score in "Mensa International Contest 2001", 1st. Place on X-Test Contest, among 2nd. and 6th. Place in "Smartest Person of the World Contest" by International High IQ Society. More about Petri. See also his comment on the new norm of the Sigma Test here.



By Albert FRANK
(this article is published in ComMensal, Papyrus and Gift of Fire)

In 1999, a tragic emptiness appeared in the world of the " great" tests : For various reasons, the Mega, the Titan, The Power, The TFG shorts form of Cooijmans stopped being valid as tests of qualification, and the numerical section of the TFG long form has been suppressed.  
This emptiness has just been heapped : Hindemburg Melao Jr., founder of the Sigma Society (index.html) has created the " Sigma Test ", after a long and serious work, both in the realization of the test that in the establishment of norms. The test is available since September 2001.  
Who is Hindemburg Melao Jr., the founder of the Sigma Society? Born in Sao Paulo (Brazil) on January 15th 1972, he is a personality known in the world of chess. Melao has two world records in chess:  
- The longest announced checkmate in a simultaneous blindfold chess game, Sao Paulo, 1997 (mate in 12 moves, playing on 9 boards). This record is registered in the Guinness Book of Records, Brazilian Edition, 1998, pages 110 - 111.  
- The longest announced checkmate in a correspondence chess game: mate in 36 moves, in Special Class Tournament CXEB, published in Pi Society Journal - 05/00.  
He has written many relevant articles in the following fields: Mathematics, Physics, Astronomy, Psychology (problems concerning gifted children), and Research about the standardization of IQ tests.  
The Sigma Test : This test consists of 36 questions. These, weighted in ten levels of difficulties, are, above all, completely varied.  
What is particularly remarkable in this test ?  
- The increasing difficulty of the questions, that goes progressively from direct reasoning problems to questions needing a high power of reasoning using lateral (or divergent) thinking.  
- The questions concern a lot of various topics.  
- Very little preliminary knowledge seems to be required.  
- The standardization, obviously result of a long and serious work, is very clearly presented at the end of the test.  
- The weighted of the questions. It is practically the first time that, in a test, the " difficult " questions have a weight that seems proportional to the work and to the level of reasoning needed to solve them.  
The world of tests must thank Hindemburg Melao Jr. for having given him this test !  
Comment sent by Albert Fank, from Belgium. Albert is international referee by specialized magazines, Professor of Logic and Mathematics at University of Brussels and passed many years in Africa, teaching Chess and Mathematics. He was national champion of Chess in several countries and holds several titles of "National Chessmaster", National Champion of Chess of Veterans in Belgium. He was also Chess Champion of Brussels, author of significant international contests of puzzles, author of pedagogical works recognized internationally (including the book "Chess and aptitude", published by the U.S. Chess Federation). Albert is pilot and flying instructor, he is founder of Ludomind, an international society for authors of difficult, beautiful and original puzzles. Albert is Honorary Member of Pars Society, member of Sigma V, Platinum Society and member of several other high IQ societies. More about Albert. See also his comment on the new norm of the Sigma Test here.

"The SIGMA test was one of the most interesting things I have done in the realm of puzzles because the later questions were so clever and had so many different levels of solution. I finished the test as a personal challenge, and it gave me great satisfaction. Some of the SIGMA test puzzles are REALLY beautiful. They are a work of art!"  
Comment sent by Peter David Bentley, from Hong Kong, is member of Sigma Society V (IQ above 180), Post-doctoral in low temperature/high vacuum Physics - Dept of Engineering Science - Oxford University, Ph.D. in low temperature/high vacuum Physics - Dept of Engineering Science - Oxford University, Managing Director of INFICON Ltd (China). Peter also is Honorary Member of World Association for Highly Intelligent People, member of Mensa-UK, was Manager of Divison of “Hong Kong Productivity Council”, General Director of “VG Instruments Asia Ltd.”, General Manager of "Leybold China Ltd." and of "Balzers and Leybold China Ltd.", Director of Projects and Manager of Sales of “Edwards High Vacuum, UK”. Peter is a world authority in puzzles, co-founder of Ludomind, author of many hard and original puzzles and quizzes, he is holder of the second highest score in Sigma Test, perfected the solution 32 of the Sigma Test and proposed a very interesting ideas on questions 29 of the Sigma Test and 4 of the Sigma Test VI.

(English Version) Dear Mr. Melao:

I found some interesting IQ test in Internet. However I have realized many of them are heavily cultural dependent. For instance, Dr. Hoefflin Power Test has rather interesting and difficult problems, however too many of them abuse of the mathematical abilities of the tester. The same problem has the test of Haselbauger and some others. I don’t mean they call for a Ph. degree in Mathematics, but it is clear than people with a strong mathematics background would get rather better scores than other people. Some others as Titan Ultra and Mega use verbal analogies which not only are heavily cultural dependent, also English speakers would get advantage from that.

The first time I saw the Sigma Test, I have to recognize that I didn’t like it as much as the Power Test or similar ones. Some ingenious problems of the second half seemed too arbitrary and without scientific interest for psicometry, as they didn’t have a unique solution and that makes me think they had a lack of objectivity. After answer questions 1 to 25 I found the others very vague. Even mathematical questions as the 31 which requires: first to figure out the theoretical model that the question is calling for and only them go for the second step: mathematically work it out. I haven’t found even one of those in Dr. Hoefflin tests, as those questions can be answered going directly to the second step.

Sigma test requires a strong convergent and divergent (lateral) thinking. Only a creative and deductive mind could get a high score in that test. If one test can tell an universal genius from other person who is only good at mathematics or verbal quizzes is the Sigma Test. Even a person without a mathematical knowledge, non native of the language of the test (no verbal analogies) could via questions 34, 35 and 36 get a very high score.

The scoring system is also new, and I am not only talking about the different weight of the questions, also as the tester has to explain the way he got the answer, eventually corrects answers the tester have gotten in a wrong way can be detected, so the IQ scores will not be dependent of the luck of the tester.

I agree with the creator of Sigma Test, the high IQ levels are more likely measured on intellectual production basis rather than using a test, however if any test can approximate better this is Mr. Hindemburg Melao Jr Sigma Test. We everybody thanks to Mr. Melao his contribution to the psicometry.

Luis Lara.

(Version Española) Querido Sr. Melao:

En Internet he encontrado algunos IQ test muy interesantes. Pero me he dado cuenta de que muchos de ellos son muy dependientes del nivel cultural del individuo. Por ejemplo el Power Test del Doctor Hoefflin, contiene unos problemas muy interesantes, sin embargo, creo que abusa de las habilidades matemáticas del que los toma. Y lo mismo le pasa a los de Haselbauer y otros más. Algunos como el Titán, Mega y Ultra contienen ejercicios de analogías que son muy culturalmente dependientes y que además serían más fáciles, obviamente, para los angloparlantes. Cuando me topé con el Sigma Test, he de reconocer que no me gustó tanto como el Power Test. Y algunos problemas de ingenio de la segunda mitad me parecían muy arbitrarios y sin interés, pues parecía que al no existir solución única carecían de la objetividad que debe de tener un IQ test. Después de responder a las preguntas de la 1 a la 25 las demás me parecían muy vagas. Pasó el tiempo y me fui dando cuenta de que el Sigma Test probablemente sea el mejor test de los que he visto nunca. El Sigma Test, además de habilidades deductivas, se ocupa del pensamiento divergente y de la creatividad, como el Power Test no podría nunca hacerlo. Las respuestas en los últimos problemas del Sigma no siempre son únicas, aunque exista una que es la mejor de todas. Creo que si un test podría distinguir entre un genio creativo como Leonardo da Vinci de una persona que simplemente tiene una buena capacidad matemática ése sería el Sigma Test. Además, al contrario que muchos otros test, personas sin conocimientos matemáticos pueden obtener puntuaciones IQ muy altas ya que las preguntas 26-30, 33-36 no requieren conocimientos matemáticos pero sí un alto, altísimo IQ para responder correctamente a las 35, 36.

El sistema de puntuación es también novedoso, permite puntuación parcial de un test para respuestas parcialmente correctas, cosa que otros test no permiten. Además, la nueva norma nos da mejores ideas acerca del IQ del testando.

La idea de que el verdadero IQ del testando, especialmente para los valores más altos del IQ, se ve mejor en la producción intelectual de la persona más que en un test de IQ me parece verdaderamente correcta. Por eso dice usted que los miembros de Mega no son tan inteligentes como un premio Nobel de ciencia medio. No obstante creo que el Sigma Test es más cercano, puede reflejar más exactamente, el desempeño mental de alguien en la vida profesional de lo que lo pueden hacer los test de Hoefflin u otros. Esto se debe a que las preguntas del Sigma no requieren un solo tipo de pensamiento sino varios, además están basadas en situaciones concretas que son ó parecen reales. Le felicito por su contribución la psicometría.

Luis Lara.

Comentários enviados por Luis Lara Dolado, da Espanha. Membro de Sigma IV, muito talentoso para Física e Matemática. Ganhou uma bolsa para estudar na China (Beijing) e se graduou em chinês moderno (katagana? hiragana?). Luis também é piloto e instrutor de vôo.

"(...) Um belíssimo exemplo de teste sem limite de tempo, com teto avaliado em 244 (sd16- p-QI) é o Sigma Teste, desenvolvido por Hindemburg Melão Jr.

Este teste é um desafio que todos deveriam experimentar, pois ao terminá-lo, certamente, você verá que as suas noções de lógica, linguagem e capacidade de enfrentar problemas estão muito melhores que quando você começou."

Fragmento extraído de um artigo de Guilherme Marques dos Santos Silva, do Brasil. Membro de Sigma V (QI>180), Platinum (QI>164), Ludomind (QI> ~160), Colloquy (QI>141), Mensa (QI>133) e Sigma (QI>132). Guilherme tem o 4o. maior escore no Sigma Test pela nova norma, foi 5o. colocado no vestibular para Engenharia da UFPR e 3o. no da PUC-PR. Guilherme é engenheiro civil e leciona Matemática, é autor de um algoritmo inovador para otimizar o tráfego de veículos terrestres, que será usado na Holanda. Mais sobre Guilherme:

Thought tests and puzzles always have amused me, this is the first IQ-test I have bothered to send in for scoring. I found myself increasingly absorbed by the intellectual art behind the questions in this test. Together with achievement, I rank creativity on top of the scale, which you elegantly have combined with divergent / convergent thinking. Thank you for creating a great test. I now look forward to take the Sigma Test VI! Provided my scores are sufficient, I intend to apply for membership in the Sigma Society.

Comment sent by Ulf Westerlund, from Sweden. Member of Sigma IV, Ph.D. in Neuroscience, MD specialist in Neurosurgery, member of AANS (American Association of Neurological Surgeons) and EANS (European Association of Neurological Surgeons).

"I would like to take the Sigma Test. (Which I believe has the best end excellent questions.)" 
Comment sent by Emrehan Halici, from Turkey, born in 1956, Electr. Engineer (B.S., M.S.), Founder and owner of the Halici Informatics and Software Group of Companies, President of Turkish Intelligence Foundation (1995-...), Vice President of FIDE - Fédération Internationale Des Échecs (1998-2002), President of Turkish Chess Federation (1991-1999), Member of The Turkish Parliament (1999-2002), Member of MENSA. More about Emrehan

"Estou gostando muito do teste SIGMA. Já o imprimi e comecei a responder suas questões. Permita-me parabenizar pelo seu teste. De facto, é incomparavelmente melhor que os testes de QI que já fiz." 
Comment sent by Renato P. dos Santos, do Brasil, é Pós-doutorado em aplicações de Inteligência Artificial ao cálculo científico em Física (Institut für Algorithmen und Kognitive Systeme, Karlsruhe, Alemanha, em 1989 e Research Institute for Symbolic Computation, Linz, Áustria, em 1990). Doutorado em Física pelo Centro Brasileiro de Pesquisas Físicas, em 1987, com uma tese sobre potencial efetivo em modelos supersimétricos quirais. Mestrado pelo IFT, com tese sobre aspectos clássicos do monopólo magnético de Dirac. More about Renato. Veja também este artigo de Renato Santos sobre sociedades de alto QI:

"After the excellent experience with Sigma Test, which I liked very much as the beauty and elegance of the questions bring a great intellectual challenge and excitement, I want to apply for membership in Sigma Society, Sigma III." 
Comment sent by Reinhard Matuschka, from Germany, is member of.Sigma Society IV (IQ>164) and Mensa (IQ>133). Reinhard is Master of Computer Science, Master of Economcs and Master of Business Administration. 

This message was published on the forum of International High IQ Society (currently "International High IQ Society") on 7/31/2001

Posted by FatalX (David Spencer) on 13:51:12 7/31/2001 from  

The Sigma Society---Creative Fusion1  

I've just translated the Sigma Society Test -- which claims to test up to IQ 202, by levels (sigma) -- into English. Though I am uncertain about the scale, (I don't believe it could differentiate any higher than the 180-190+ level) the test itself is almost a relief.  

The problems are almost Pascal-like and highly creative. The test begins with basic Mensa/WAIS/Binet questions, which progressively turn into more interesting problems like correcting a false conclusion about Fermat's Theorem deriving from the Pythagorean, measuring lung capacity within a $ budget, approach diameters for a planet (from a parachute POV), weighing the Graphite on a piece of paper, developing methods for estimating a stranger's vocabulary, getting out of a cannibalistic situation by picking eggs and constructing a Sphere of Invisibility. 

Now I may be mistaken, but these seem much closer to the problems for which Vinci and Pascal are famous. 

Creative and Logical, with a high degree of unconventional thought required. I hear it's decently normed, too -- 

Email me if you want a copy of the translation. 

Comment posted by David Spencer (FatalX), from U.S.A., is one of the most outstanding members of the International High IQ Society. He is recognized in the community of high I.Q. for his high creativity and his perspicacious comments

Dear Christian, I lost your comments. :-( Please, send it again. Thank you! Melao

Comment sent by Christian Hohenstein, from Germany, Ph.D., member of Sigma IV (IQ>164) and High Potentials Society (IQ>133)

"This Sigma test is beautiful. I have never seen anything like this before. It is not an ordinary IQ test but a masterpiece in the art of testing a human's ability to solve the indissoluble. Wonderful Melao:)" 
Comment sent by Muhamed Veletanlic, form Sweden, member of Platinum (IQ>164), Sigma IV (IQ>164), ISI-S (IQ>151), Glia (IQ>150), Cerebrals (IQ>144), Poetic Genius Society (IQ>141), Existentia (IQ>137), High Potentials Society (IQ>133), VINCI (IQ>126), International High IQ Society (IQ>126), Order of Imhotep. M.Sc. in Electrical Engineering.

"The Sigma Test is undoubtedly the hardest intelligence test that I've encountered so far. I've enjoyed it a lot though as it is comprised of ingenious questions that could measure the depth of one's mathematical and logical reasoning abilities."

Comment sent by Nileon M. Dimalaluan Jr., from Philippines, member of ISI-S (IQ>151),
CIVIQ Society (IQ>150), International Society for Philosophical Enquiry (IQ>150), Cerebrals (IQ>144), Sigma Society (IQ>133), High Potentials Society (IQ>133), VINCI (IQ>126) and International High IQ Society (IQ>126). He has a very high score in W-87 and very high scores in N-VCPE-R, X-Test, IHIQS Ultimate Test e SLSE-Form I.

"I also want to say to you that the Sigma Test is incredibly brilliant. It was by far the best test I have ever taken and enjoyed it very much."  

Comment sent by Dylan Taylor, from USA. He is MD and works with financial consultancy, has excellent scores on SAT and other tests, highest score on English version of the Giant Test given by the High Potentials Society. Dylan is member of ISI-S (IQ>151), CIVIQ Society (IQ>150), Glia Society (IQ>150), Sigma III (IQ>148), Cerebrals (IQ>144), Poetic Genius Society (IQ>141), Existentia (IQ>137), High Potentials Society (IQ>133), Mensa (IQ>133), Mysterium Society (IQ>132), VINCI (IQ>126).

"I must say I thoroughly enjoyed this test. It was incredibly challenging and it has pushed my abilities to their outer limits." (...) "I have put more effort into this test than any other, and have even lost a few hours of sleep mulling over some of the toughest questions. My favorite question was #32. I am looking for this test to give me a good indication of what my true capabilities are. I believe I can go beyond Mensa and qualify for Sigma III, or perhaps even higher. Please accept this exam as my best effort, as much time and work have gone into it. Thank you!"

Comment sent by
Wade Graydon Penman, from Canada, member of Sigma IV (IQ>164), former member of Mensa (IQ>133).

"I am very pleased with the result esp. because it is a good result on without a doubt the best test to be found on the web." (...) "It was for me a true pleasure to take it, as it was both challenging and fun. The Sigma Test is simply a beatiful test"

Comment sent by
Bart Lindekens, from Belgium, member of Sigma V (IQ>180), Platinum (IQ>164), Ludomind (IQ> ~160), ISI-S (IQ>151). He works as a risk manager (bank). He has one of the highest scores on the Sigma Test (3rd place in the old norm).

"Thank you for a fascinating, thrilling and a very challenging test! I will recommended it to friends and colleagues who might be interested in this kind of challenge. My next mission will be Sigma Test VI."  

Comment sent by Kristian Heide, from Norway, excellent score on Titan and other tests, member of Sigma Society IV (IQ>164), One-in-a-Thousand Society (IQ>150), Mensa-Norway (IQ>133), Ph.D. Student and M.Sc. in Astrophysics, previous national record holder in egg throwing (1992-96). About this record, Kristian comment: "I guess that gave me an advantage on problem no. 34 on The Sigma Test ;-)." He is creator of an innovative system for sporting ranking, creator of a new method for ranking of Think Fast. See also his comment on the new norm of the Sigma Test here.

"I've been having a look over The Sigma Test (which is a much respected test) and have decided I will have a go at it this year. Everyone in IQ land should try this test, I think!" 

Comment sent by Michael Dempsey, from United Kingdom, member of Platinum (IQ>164), ISI-S (IQ>151), Glia (IQ>150), CIVIQ (IQ>150), Sigma III (IQ>148), Mensa (IQ>133), Mysterium (IQ>132)) and International High IQ Society (IQ>126). Michael is Honours degree B.Sc. in Chemical Analysis.

"Soy un reciente miembro de Sigma Society. Acabo de ver publicadas en la página de la organización las correlaciones existentes entre el sigma test y otros tests. Estoy de acuerdo en algunos principios que inspiran el Sigma Test, tales como que hay que premiar el razonamiento profundo sobre la rapidez, que las preguntas de elección múltiple dan lugar a aciertos 'accidentales', etc." 

Comment sent by Emilio López Aliaga, da Espanha, é membro de Sigma Society IV, da Mensa e programador da Copo Thierry, S.A

"I am currently working on your excellent Sigma Test. I am enjoying it very much."  

    Comment sent by Kaj Forsell Bio (Kaj by Kaj): 
    Born in Helsinki, Finland, 48 years ago, I have spent the last 25 years living in Sweden, Norway, UK, USA and Japan. I have a Business Degree from Stockholm University.  
    Career sofar: I like variation so I have covered many areas in the business world starting out as a public accountant and moving to financial management positions in a variety of industries, from finance to powergeneration and mobile phones. Currently I am President of a Software development and sales company in Japan.  
    I also enjoy different cultures which is why I have chosen to live in many different countries.  
    Hobbies and interests include food and drink, music (listening and playing the guitar), current affairs, surfing on the net and knowledge in general. I also have an aspiring interest in chess. When I have time and want to be outdoors I like to play golf. If you like challenging sports, this is it. The late Sir Winston Churchill already said that it's an impossible game with impossible tools. He might not have been the gratest atlhlete, but there's something to what he says.

"I enjoyed very much working on this test, it was fun." 

Comment sent by Staffan A. Svensson, from Sweden, is member of Sigma Society V (IQ>180), Prometheus (IQ>164), Ultranet (IQ>164) and Mensa (IQ>132), he have excellent score on several tests and highest score on the LS-36. 

From Stephen Reejis (United States, Boston University, member of Cerebrals Society):


Thanks for the detailed statistical information pointers. Rarely does one get in these or even non-statistical but scientific circles the breadth of coverage you have touched upon. But frequently "scientists" make all sorts of statistical inferential slippages, although what everyone remembers is only the "punchline" of their papers. This is very useful exposure, and I will try to delve into many of the areas you have brought up.

A few of the links don't work though. The other links are very good.

And since you are here, although I have not submitted the original Sigma test (not that much money ), I must say that it is a completely beautiful excercise. I really appreciate the degree of thought that goes into the items and it has given me a lot of pleasure to think about some of the items ( I particularly like the one about the boiled/unboiled eggs with the cannibals) and a few others at that level (although the hardest ones have me perfectly stumped). I have two silver math IMO friend and an applied math major friend and in my mind, the quality of their general thought and ability is amazing (I am a strong believer that mathamatical ability is the strongest marker for intellect, very beautifully tested in IMO-style questions). Your test combines creativity and brings a tangibility to exactly what is the complexity involved in an item of high difficulty, and makes the item accessible to the non-specialist (contrast with IMO questions, which require at least a basic understanding of some areas). Congratulations to you for it


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