Here is a well-defined strategy game played out in CBS’s Survivor in Thailand.

The Game

There are 21 flags planted in the field between two ‘tribes’ – Chuay Gahn and Sook Jai. Each tribe takes turns removing flags. Each tribe at its turn can choose to remove 1 or 2 or 3 flags. The team to take the last flag, whether standing alone or part of a group of 2 or 3 flags, wins the game.

The first tribe – Sook Jai – chose to remove 2 flags. Was this the right move?

Clue

During the discussion within one of the teams, Ted Rogers – an African American software developer, said:

At the end, we must leave them with four flags.

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Four angels sat on the Christmas tree amidst other ornaments. Two had blue halos and two yellow. However, none of them could see above his head.

Angel A sat on the top branch and could see the angels B and C, who sat below him. Angel B, could see angel C who sat on the lower branch. And angel D stood at the base of the tree obscured from view by a thicket of branches, so no one could see him and he could not see anyone either.

Which one of them could be the first to guess the color of his halo and speak it out loud for all other angels to hear?

From Brainden.com

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What is Mensa

Founded in 1946 by Roland Berrill, an Australian barrister, and Dr. Lancelot Ware, a British scientist and lawyer, Mensa is a high IQ society – the only qualification for membership being an IQ is in the top 2% of the population.  Mensa members are also known as ‘Mensans’.

The word ‘Mensa’ comprises two Latin words: mens, which means “mind” and mensa, which means “table”, indicating that it is a round-table (open discussion) society of minds.

There are now around 100,000 Mensans in 100 countries throughout the world. There are active Mensa organizations in over 40 countries on every continent except Antarctica.

The website for Mensa International can be found here.

Websites for national groups can be found here.

What are the advantages of being a Mensa member?

1. Intellectual stimulation. You can find intellectual resources to exercise your brain in national magazines, in local newsletters, and at regional, national and international conventions. Mensans (Mensa members) have a profusion of special interest groups. To quote from Mensa International:

Whatever your passion, there’s almost certain to be a Special Interest Group (SIG) filled with other Mensans who share it! Mensa offers approximately 200 SIGs, in mind-boggling profusion from African Violets to zoology. Along the way you’ll find microbiology, and systems analysis, but you’ll also find Sherlock Holmes, chocolate and Star Trek. There are the expected: biochemistry, space science, economics — and the unexpected: poker, roller-skating, scuba diving, UFOs and witchcraft. There are SIGs for breadmaking, winemaking, cartooning, silversmithing, and clowning. Heraldry, semantics and Egyptology co-exist with beekeeping, motorcycling and tap dancing. Sports SIGs cover the classics (baseball, basketball, and football) and the not-so-classic (skeet shooting, hang gliding, skydiving). And any Mensan who can’t find a SIG to join can easily start one.

2. Social life. Local groups meet monthly or even more regularly. There are widely attended annual conventions offering workshops, seminars, and parties.

3. Mensa publications. You will receive your national magazine with contributions by Mensans on a wide variety of subjects. In some countries, in addition to the national magazine you may receive lively local newsletters. Mensa also publishes it’s own research journal on IQ related topics – The Mensa Research Journal – for the general public. http://www.mensafoundation.org/AM/Template.cfm?Section=Journal

4. Miscellaneous benefits. In some countries Mensa sponsors a members-only credit card and insurance program. There is also a program that aids traveling Mensans. There have been reports that job applications have been easier with Mensa membership on your CV – particularly if the hiring person is also a Mensan.

How to become a Mensa member?

Mensa membership is open to people who score at the 98^th percentile or higher on a standardized, supervised intelligence test.

American Mensa accepts scores from approximately 200 different standardized intelligence tests, as well as Mensa’s own dedicated IQ test. Some of these test one’s spatial and analytical abilities using non-verbal questions only. We call these tests “culture fair” because they don’t require general knowledge, vocabulary or math skills that are learned in school and which differ from culture to culture. Other IQ tests include questions that present verbal analogies or puzzles that test comprehension and mathematical ability.

A list of some of the authorized IQ tests for Mensa membership with Mensa membership are listed here.

Results from tests given by an institution, agency or clinic must include the full name of the test, the score and the percentile rank. This documentation must be on the letterhead of the institution, agency or clinic; it also must be signed by the psychologist responsible for the testing and must include the psychologist’s license/certification number as issued by the state in which the psychologist practices. Applications are individually assessed by Mensa. The American Mensa application form can be found here. This month the evaluation is free. Normally it is $40.

You may already be qualified!

If you took your SAT exam before 1/31/94 or GRE before 9/30/01 you may find your score qualifies you for membership. For details click here.

Mensa Admission Test

If you have not taken an official IQ test by a qualified administrator, you can choose to take Mensa’s own Admission Test.  This involves certified volunteer Proctors supervising a testing session in your area! You can contact your national Mensa organisation to find out about the schedules for these tests – click here for details.

If you score at or above the 98th percentile on either of the two tests, you’ll qualify and be invited to join Mensa.

If English isn’t your primary language, American Mensa offers a battery of culture fair, non-language tests.

How to prepare for an IQ test to join Mensa

This will be the topic of our next blog. Practice makes a very big difference.  Improving your fluid intelligence with High IQ Pro® training will also help substantially.

To get you limbered up, try the Mensa Workout.

Or take the Mensa home test.

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Here is a traditional Raven’s Advanced Progressive Matrices test item. This kind of test item is often used in job aptitude tests.

Why do we use this kind of test question for our pre- and post-training IQ test?

Matrix items are a reasoning task using figures.  They offer these advantages over other IQ-related tasks (listed below) and for this reason they are a good test for an overall assessment of general intelligence, and are a popular choice for job aptitude tests.

• Matrix items have been found to measure central analytical processes (g; Kyllonen & Christal, 1990).
• Correspondence finding and goal management processes are involved in the cognitive mechanisms addressed with Matrix tests (Carpenter et al., 1990).
• Matrix questions are among the intelligence task types considered to be culture-fair, as they do not rely on verbal information (e.g., [Cattell, 1979] and [Corman and Budoff, 1974]). (For verbal intelligence measures and training, there are the resources of i3 Mindware.)
• Matrix items can be generated automatically because a rational item construction framework can be established (e.g., [Embretson, 1998], [Embretson, 2002] and  [Freund et al., 2008]).  The generation of an unlimited number of items thus becomes feasible, and item-writer idiosyncrasies can be avoided
• The nature of Matrix items makes intuitive sense for the test-taker in understanding why this kind of test measures their IQ.

Here is a more complex, computer generated Matrix test item:

click to enlarge

Scientific reference source for this article here.

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In the square of 64 slots there are 34 hidden consecutive associations which you must discover. An association is a coherent relation between two adjacent slots or two slots that are connected diagonally.

The slot of origin is e-3, from here you must choose the next slot (and always one at a time, without skipping) in the direction you consider most convenient (right, up, left, down or diagonal). Keep in mind that there are 30 slots that don’t contain a real useful relation.

Each correctly chosen association is worth a point.

One error is permitted in the sequence of associations. Only the points obtained in a consecutive manner starting from the slot of origin will be counted.

The associations need to be described through letters and numbers. For example: c6-d7

Some associations require convergent thinking and others powerful divergent thinking. In general, logical, numerical, symbolic and spatial connections are presented. Alternative thinking is the key to success. Keep in mind that despite the “ameable” aspect of the test, it is highly challenging. Work as had as you can.

Required cultural level: medium

Estimated time for complete resolution: between 2 and 4 hours.

Send your answers to: hiqland@gmail.com

A few days after your answers have been received you will be e-mailed a score report.

Take as much time as you need.
References are allowed.
Please, do not discuss solutions in public forums.
No norm is available yet.

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These puzzles involve looking at the problem from an unexpected viewpoint – sometimes known as ‘lateral thinking’.

There is a barrel with no lid and some beer in it. “This barrel is more than half full of beer,” said Chuck. “No it’s not,” say Joe. “It’s less than half full.” Without any measuring implements and without removing any beer from the barrel, how can they quickly and easily determine who is correct?

Three switches outside a windowless room are connected to three light bulbs inside the room. How can you determine which switch is connected to which bulb if you are only allowed to enter the room once?

——–

Answers below:

The Barrel

There is a barrel with no lid and some beer in it. “This barrel is more than half full of beer,” said Chuck. “No it’s not,” say Joe. “It’s less than half full.” Without any measuring implements and without removing any beer from the barrel, how can they quickly and easily determine who is correct?

Answer

My initial answer was to assume that the barrel symmetrically bulged and if you placed it up against something vertical, the point of contact marked the half-way point. But this is too awkward. The simple answer is tip the barrel until the beer reaches the rim. If you can see the bottom, then the barrel is less than half full; otherwise not.

Switches

Three switches outside a windowless room are connected to three light bulbs inside the room. How can you determine which switch is connected to which bulb if you are only allowed to enter the room once?

Answer

Say you have left (L), middle (M) and right (R) switches outside. If you turn L on, you know that the light that is on in the room corresponds to L. But what about the other two lights? To answer this you need to think laterally – about properties of lights. Turn M on for a couple of minutes, then off. Then go in the room, and feel the two light bulbs that are off. The warm one corresponds to M, the cold one to R!

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• British Mensa Puzzles and Mensa IQ Tests - From British Mensa
• Mensa Brainteasers - From British Mensa
• Mensa Prize Puzzle Competition - From British Mensa
• Monthly Puzzle - From Mensa in Canada
• Puzzles - From Mensa in Hong Kong
• Math Puzzles - From Spanish Mensa Magazine
• Games Room - Puzzles from American Mensa

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Matrix Reasoning problems are one of the best ways to measure our fluid intelligence. The famous ‘Ravens Matrices’ IQ test (standard and advanced) – which Mensa accepts as a qualifying IQ test – are made up of ONLY matrix reasoning problems. All IQ tests have a section for these types of problems. This problem set is from Bergman Data and Smartkits.com.

These types of problems are often used in job aptitude (psychometric) tests.

Try to complete all problems in half an hour. Most of these types of questions have time limits, so it is advised to work through them with a sense of limited time. If one is taking time, skip it and return to it later. They tend to get more difficult as they go along. Getting practice in these problems will help your performance in any IQ test. If you get 6-9 correct you have a chance at Mensa with some training; if you get 10-12, you should not struggle with the Mensa challenge.

There has been a change in some of these questions, to get a more representative variety of questions! If you were working on the older set, I can provide answers for those too!

Answers will be provided next week.

ARE YOU READY?…

2.

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3.

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4.

_________________________________________________________

5.

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6. What figure should come next (after e)?

_________________________________________________________

7.

_________________________________________________________

8.

_________________________________________________________

9.

_________________________________________________________

10. Which one is NOT part of the series?

_________________________________________________________

11.

_________________________________________________________

12.

.______________________________________________________________

Answers for the Matrix problems in this post.

1. 7, 2. D, 3. A, 4. D, 5. A,  6. 1, 7. 1, 8. B, 9. 5, 10. 1 OR 5 (did anyone spot this?). 11. 5, 12. C.

Note that with 10, you may have found an answer, and assumed this was the only answer, but two answers are in fact possible.

You can see explanations for most of these answers here.

Solving these kinds of problems requires finding underlying rules. Here is an example from a famous IQ test called Raven Advanced Progressive Matrices:

1.  Each row contains 3 shapes (triangle, square, diamond).

2.  Each row has 3 bars (black, striped, clear).

3.  The orientation of each bar is the same within a row, but varies from row to row (vertical, horizontal, diagonal).

From these 3 rules, the answer can be inferred (5).

Feel free to leave your answers as a comment. If you are interested in more IQ test questions – click here.

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Sudoku historical background

Like the cross-word puzzle, Sudoku is a game with a grid and a simple set of rules, generating infinite possibilities. Unlike the crossword, Sudoku doesn’t require any ‘cultural knowledge’ (general knowledge and language ability). It just requires putting numbers in cells in a logical way. Psychologists distinguish between two types of intelligence: crystallized and fluid. Crystallized intelligence depends on general knowledge and language. Fluid intelligence depends only on reasoning ability. Sudoku is a fluid intelligence puzzle.

Sudoku is Japanese for ‘only single numbers allowed’. In spite of its Japanese name the puzzle was first invented by the architect Howard Garns in the United States, appearing for the first time in May 1979 in the Dell Pencil Puzzles and Crossword Games magazine. Five years later, an editor for Niloli magazines in Japan noticed the puzzle and published it in his magazines under the name Sudoku. It then went viral in Japan. A retired New Zealand judge noticed what was going on in Japan and published some of the puzzles in the Conway Daily Sun of New Hampshire in 2004. After this, Sudoku puzzles appeared in The Times of London, and soon went viral in the UK, and then the world. Sudoku puzzles are now a permanent feature of puzzle pages in newspapers.

What is a Sudoku puzzle and how do you solve one?

A Sudoku puzzle is made up of a 9 x 9  grid, with heavy lines dividing it into nine three-by-three boxes. The challenge is to fill it with digits from 1 through 9, so that every three-by-three box, every row, and every column contains these 9 digits, without repeating – once and only once. An example of completed Sudoku puzzle is shown below to show you how this works. Notice that in each small 3×3 box, you find 1 through 9, as well as in every row and every column of the 9×9 grid.

The puzzle-maker provides some of the numbers which give the clues to be used in solving the puzzle. The fewer initial numbers that are given, the harder the puzzle.  Here is a puzzle of moderate difficulty provided by puzzle master Dr. Marcel Danesi:

The solution involves logical thinking-deducing where numbers can or cannot be placed. For example in the 3rd row, the 2 spaces must be filled by either a 2 or a 4. Which number goes where? If you look at the top right 3×3 grid, you know that the middle blank cannot be a 4 because there is already a 4 lower in that column. So you can conclude that it must be a 2. Therefore the other blank must be a 4. The first blank on the 3rd row must therefore be a 2. With this extra information, you can start to figure out other numbers through similar logical reasoning. The answer to this puzzle will be given in a few days.

Benefits of Sudoku for Alzheimer’s prevention

The United States’ Alzheimer’s Association has endorsed Sudoku as a preventive brain training exercise against Alzheimer’s. Their recommendation is based on published studies, which suggest that Sudoku may help prevent dementia.

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…..

To help us understand the elements of this skill set, take question 26 in the Mensa workout. Notice the line in the bottom left corner and ignore the other stuff; in the next square it’s in the top right corner, then it’s back to the bottom left, then up again to the top right and so on. There’s a pattern. So you can reason that the answer has to be b or c. Hold that in mind. Now look at the bottom right corner line. Next square there are two lines in the top left, next box there are three lines bottom right, next box four lines top left, then five bottom right. So the next has to be? Six lines top left. Only a and c show this. From before, we know that it can’t be a. So we can conclude right there – without even looking at the other lines in the box, that the answer is c.

To solve this kind of problem we need to use what cognitive psychologists and neuroscientists called executive processes. With executive processes we can’t rely on an automatic response based on past experience to solve a problem – we have to reason it through with full attention.

Elements of executive processes

• We have to selectively attend to some information and ignore distracting information.
• We have to hold items of information in short term memory (what is known as ‘working’ memory’).
• We have to do mental operations on the information  (e.g. ’add one’) and update the information we are attending to as we are working through the problem.
• We also have to break the problem down into sub-tasks  and be strategic with our effort in different sub tasks. For  instance, there was another sub-task we could have done – looking at the other set of lines – but we didn’t have to look at them. This involves monitoring how we’re doing on the task by observing how our own mental processes work.

All these cognitive skills are the elements of executive processes. They lie at the heart of the ‘brain power’ aspect of what IQ tests measure. If a person  is good at  doing these things, the have more brain power.  And they will do well on the matrices sections of an IQ test.

The very good news is that our IQ can be increased  not only by improving by practicing these problems – there is a BIG practice effect for all IQ test questions – but also by training our executive processes. By training our executive processes we actually increase our fluid intelligence and brain power. We become ‘smarter’ in the most basic sense – better able to process any kind of information, and solve any kind of problem, not just ones we have prior knowledge about.

How improve IQ by training our executive processes

In 2008 brain scientists at the University of Bern in Switzerland and the University of Michigan in the States, demonstrated that training on a carefully designed exercise that directly trains these working memory elements,  resulted in a remarkable 40% gain in fluid intelligence as measured by a version of the time limited Raven’s Advanced Progressive Matrices test – a test with questions just like the ones above.

We provide this exercise in the professional software package High IQ Pro®.

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