One of the stereotypical views (indeed prejudices) about project managers is that they are all left-brain thinkers: “all about process, never about creativity or imagination”. I learned at an early stage in my career that the effect of reciprocity means that people will behave in the way that you treat them; so treat someone as if they are not creative, an enemy of innovation and change and they will, indeed, behave in that way.

To lighten the tone before Christmas, I am sharing an extract from Ian Stokes’ wonderful collection: Training for Project Management. This activity includes a whole range of brain-teasers, conundrums and other little exercises designed to stimulate both left- and right-brain thinking.

Team Brain Teasers


Brain-teasers are always useful because they help us to come to terms with the different ways in which people think. And we can even surprise ourselves by the judgements we take, the understanding that we develop and the perceptions that reveal our thought processes.


One person exclaims, ‘I haven’t understood anything that you’ve been saying for the past five minutes.’ And the other replies, ‘Well, I really don’t understand what you don’t understand about what I’ve been saying.’ Clearly, not much is going to happen very quickly.

It’s a situation that gets repeated again and again in business. One group thinks that the other group lives in the clouds. The second group thinks the first don’t live in the real world of flesh and blood. The result? A ‘them and us’ situation.

If people are to work together, they need to understand each other, and, to understand others, we need a better understanding of ourselves and how we think.


  • To develop understanding of the way in which we think and make decisions.
  • To explore thinking patterns and comprehend some thinking traps.
  • To heighten awareness about critical thinking.

Trainer guidance

Our thinking can often lead us astray. The way we think about probability is one way in which we can confuse our thinking. This is illustrated in the first four brain-teasers.

Since we think in terms of probabilities every day, it may seem strange that we can be led so easily into error. But, there are some clear explanations for this. One is our tendency to use percentages, which are less obvious than propensities. A percentage indicates 18 per cent, where a propensity says 1 out of 6, which is the same thing, but 1 out of 6 appeals much better to our intuition. This is demonstrated in the second brain-teaser, ‘False-positive test’.

It’s hard to take adequate account of factors such as sample size, as in the example of sumo wrestlers and swimmers. And it’s not so obvious to judge whether information that we are receiving is driven by random factors, or by deliberate choice, as in the Monty Hall problem.

The Babe Ruth and Lou Gehrig riddle also seems far from intuitive. It shows how we can be fooled by our expectations, which would be a problem for a project.

The second group of brain-teasers  are all about logic. When it comes to questions of logic, a little method can go a long way. These brain-teasers show us that if we don’t have the right method available, then even simple-looking conundrums can chew up a lot of thinking time, with a potential to cause confusion.

‘Two men at a fork in the road’, ‘Cakes’ and ‘Camels’ are ancient logical brain-teasers. ‘Wolves and sheep’ looks fairly familiar, but we discover that the problem is slightly asymmetrical and therefore not quite like those we have encountered in the past. Sometimes, we have to deconstruct one way of thinking in order to reconstruct a fresh logic path.

It is best to use brain-teasers one at a time, or in groups of two or three, to avoid ‘brain-teaser fatigue’. It is also a good idea to select brain-teasers from each of the two groups so that participants can practice two different ways of thinking.

‘Thinking about thinking’ is a way of offering the participants food for thought beyond the brain-teasers.


  1. Decide how and when you are going to introduce the brain-teasers into a training course – whether you are going to support a session on a given subject or whether you intend to use the brain-teasers as energizers.
  2. Make sure that you understand the answers to the brain-teasers that you are going to use and that you know how to explain them.
  3. Announce the brain-teaser. Read out the selected brain-teaser slowly, twice, and write it up or draw it on a flipchart if necessary.
  4. Allow sufficient time for everyone to absorb the problem, give it some thought and, if possible, arrive at a solution.
  5. Ask for the answer. Discuss how the answer has been arrived at and give the correct solution if necessary.
  6. Distribute ‘Thinking about thinking’, as an afterthought.

Learning messages

Thinking clearly needs as much time and effort as any other skill. Thinking needs to be learned and perfected.


Total = about 30 minutes, depending on the selection of brain-teasers used:

  • 10 to 20 minutes to work out, discuss and explain ‘Monty Hall’, ‘False-positive test’.
  • 2 to 5 minutes for each of the other brain-teasers.


Probability and Calculation Puzzles

 The Monty Hall Problem

You are on a game show, and you are given the choice of three doors. Behind one door is a car; behind the others, goats. You have a one in three chance of picking the right door and winning the car. You pick a door, and the host, Monty Hall, who knows what is behind the doors, says, ‘I’m going to open one of the other two doors.’ He reveals a goat. Now he asks, ‘Do you want to stick with your original guess or would you like to switch to the other door that’s still closed?’ What do you do? Do you stick, or do you switch?


You should switch. If you stick with your choice, your chance of getting the car is 1 in 3, whereas if you switch after one ‘wrong’ door has been eliminated, your chances of getting the car are 2 in 3.

According to the New York Times, the problem and solution were ‘debated in the halls of the Central Intelligence Agency and the barracks of fighter pilots in the Persian Gulf’ and ‘analyzed by mathematicians at the Massachusetts Institute of Technology and computer programmers at Los Alamos National Laboratory in New Mexico’.

Once again, it’s a matter of putting yourself in someone else’s shoes. Imagine that you are Monty Hall. There are, in fact, three possibilities on the first choice:

  • a) The contestant chooses a goat.
  • b) The contestant chooses a goat.
  • c) The contestant chooses the car.

When (a), Monty has revealed goat (b), and is desperately hoping you will stick with goat (a). When (b), Monty has revealed goat (a), and is desperately hoping you will stick with goat (b). When c), Monty has revealed either goat (a) or goat (b) and is hoping you will switch.

Therefore in two cases out of three, you should switch. The game is in your favour! (We are rather unused to gambling games that play in our favour!)


False-Positive Test

You are given the following information:

  • (a) In random testing, you test positive for a disease.
  • (b) In 5 per cent of cases, this test shows positive even when the subject does not have the disease.
  • (c) In the population at large, one person in 1000 has the disease.

What is the probability that you have the disease?


Nearly everyone replies ‘95 per cent’. This is not quite right. The answer is 2 per cent.

To see why, consider a population of 1000 people:

  • 1 person out of 1000 will test positive because they really have the disease.
  • 50 people out of 1000 will test positive, without having the disease.
  • Therefore, 1 person out of 51 tests positive, because they actually have the disease.

The key is to see that the information in (c) is crucial. Most people think it irrelevant: the test is ‘95 per cent reliable’ and that’s that. Try this one on doctors. It deflates their egos wonderfully: they do hardly any better than laymen. In a study carried out in the 1970s, 80 per cent of those questioned at a leading American hospital gave the wrong answer, most of them saying 95 per cent.

Furthermore, people are easily misled by percentages as opposed to whole numbers.


Sumo Wrestlers and Swimmers

Kevin weighs 130kg and has very strong legs. He is either a sumo wrestler or a swimmer. Which is he more likely to be?


Your answer may be that George is a sumo wrestler, because he seems to fit that profile more than that of a swimmer. But this answer is wrong. There are more 130kg swimmers with strong legs in the world than there are 130kg sumo wrestlers with strong legs. That is because there are very few sumo wrestlers compared to swimmers, even though there are a much greater proportion of 130kg contestants among them than among swimmers.


Babe Ruth and Lou Gehrig Riddle

Babe Ruth and Lou Gehrig were baseball players in the first half of the twentieth century. They each set several Major League and American League records. One year, their batting averages for the first and second halves of the season were:

  1st half of season Average 2nd half of season Average
Babe Ruth 55/160 0.344 60/240 0.250
Lou Gehrig 82/240 0.342 38/160 0.238

Who has the better batting average over the whole season?


You can see that Babe Ruth’s batting average for the first half of the season, at 0.344, is slightly better than Lou Gehrig’s at 0.342. And for the second half of the season, Babe Ruth’s batting average is slightly better than Lou Gehrig’s at 0.250, compared to 0.238.

Therefore, who should have the best batting average over the whole season? It must be Babe Ruth, since his average is better for both of the two halves.

Well, no. In fact the answer is Lou Gehrig because, over the whole season, he actually hit more home runs!

Babe Ruth’s average for the whole season = 115/400 (0.288)
Lou Gehrig’s average for the whole season = 120/400 (0.300)

Funny subject, maths, isn’t it?


Logical Conundrums

Two Men at a Fork in the Road

Travelling to a city, an old man lost his way. He came to a fork in the road and did not know which road to take. Standing at the fork were two men. Next to the men was a sign, which you may assume is correct, stating that one of the two men always told the truth and one of the men always told lies (but it was not known which was which). The sign went on to say that travellers could ask only one of the men only one question. How can the old man find out which is the road to take?


Ask one of the men what the other man would answer to the question, ‘Is the left road the correct road?’ Then assume the answer that you are given is false and act on that knowledge.

If the man you ask is the liar, he will incorrectly give you the truthful man’s answer. If the man you ask is the truthful man, he’ll correctly give you the liar’s wrong answer.



You are given eight cakes. The cakes all weigh the same except for one, which is heavier. You have a balancing scale at your disposal. What is the minimum number of weighings required for you to pick out the heavy doughnut every time?


Two. Weigh three of the doughnuts against three others and leave the remaining two on the table. If the scales are even, the heavy doughnut is one of the two on the table – weigh them to find out. If the scales are uneven, take the three doughnuts on the heavy end, weigh one of them against another and leave the third on the table. If the scales are uneven, you have found the heavy one. If not, the heavy one is the one on the table.



An Arab sheikh is old and must will his fortune to one of his two sons. He makes a proposition. His two sons will ride their camels in a race, and whichever camel crosses the finish line last will win the fortune for its owner. During the race, the two brothers wander aimlessly for days, neither willing to cross the finish line.

In desperation, they ask a wise man for advice. He tells them something. The brothers leap on to the camels and charge towards the finish line. What did the wise man say?


The rules of the race were that the owner of the camel that crosses the finish line last wins the fortune. The wise man simply told them to switch camels.


Thinking About Thinking

Values and Perspectives

At the root of it all are people’s interests and their beliefs. Change is not always resisted if it is in people’s interests, but it carries the costs of uncertainty. There is usually a credibility issue as well as the questions: ‘What’s in it for me?’, ‘Is this sufficiently important?’ and ‘Is this the best way to go about it?’ Converting a strong belief that serves a purpose can be like shifting the Eiffel Tower slightly to the right. It’s best to get to the heart of the matter, to understand and to address the interests as soon as possible.

Optimism and Pessimism

An individual’s response to the famous conundrum of whether the glass is half-full or half-empty reveals an optimistic or a pessimistic view of the situation, and this can be a result of experience, mood, personality or context. People want the sales arguments. They want to hear about the benefits and the costs, for whom and when.

Pros and Cons

Listing the pros and cons, weighing them up, showing them visually as opposing forces, thinking about who is concerned, how to defuse the negative forces, how to boost the positive forces: this is the yin and the yang of project management. If there were no obstacles there would be no project. The team can develop cohesion by unifying their efforts against adversity and by harnessing support.


At the top level of priority, the entire project could be at risk. At the lowest level of priority, it could be a purely cosmetic issue. A sense of proportion is needed. There is no point throwing huge quantities of resources at a problem that is of little value. The kinds of question that need to be asked are:

  • What will be the consequences?
  • If it were to be of any use, what would it do?
  • What is the minimum that it has to do to be useful?
  • If you could resolve one problem today, what would it be?
  • If the team had 1000 ($/€/£) to spend on the project, how would they allocate the funds?


It’s surprising how real it feels when you have the money in your hands. People are reticent about parting with something tangible.

Cause and Effect

There can be one cause for many effects and many causes for one effect, just as easily as there can be many causes for many effects, or one cause for one effect. Furthermore, there can be a whole chain of causes and effects, one leading to another like a ripple effect with gradually diminishing impact, or chaotic effects where a barely perceptible cause amplifies into a shattering or breathtaking effect downstream. This is the business of quality at one end and of systems at the other.

High- and Low-Level Viewpoints

The high-level view is the big picture. It’s distressing to hear someone claim that the big picture won’t interest the grassroots, because it will only worry them. There are many people at grassroots level who are unable to function effectively without the bird’s-eye view. Similarly, there are people at the top who prefer to fulfil the role of experts and to concentrate on the detail. Nothing can be assumed. People should be asked what they prefer. It’s the first step to understanding the way people prefer to perform.

Degrees of Truth

If an expert says something does that make it true? Does anecdotal evidence have any value? What is the nature of truth? Is truth an absolute? How can you condemn something that is not wholly verifiable, but has been proven in every known instance of a statistically significant sample? How can you deal with something that may be partially true, but has delivered positive results despite running counter to all previous experience? What may be true in one situation may be false in another. People drive on the left or on the right. Water boils at 100°C (but only at sea level). Under what circumstances is it more ethical to protect someone, or to uphold a rule?

Hypothesis and Speculation

Sometimes it is important to dream as if there were no obstacles, just blue sky: ‘If we could do anything we wanted, what would it be?’ It’s more difficult than it sounds. Knowing what we really want is the hardest thing of all. It’s useful when projecting ahead into the future to idealize a situation, remove significant problems and imagine what would be done if there were no inherited constraints.

Adapted from Training for Project Management, Volume Three, by Ian Stokes, Gower Publishing, Farnham. Read and use the whole volume at www.gpmfirst.com where you can share your own favourite training tips, techniques and games.