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BRAIN TEASERS
1 - Client Decision Process
You have a really odd client who informs you that the following decision process will be used to determine whether you win or lose a large and highly profitable contract.
Two papers – one with WIN and one with LOSE typed on it – have been folded and placed in a hat. You have to pick out one of the papers (without looking). If you choose the one with WIN written on it, you get the contract. Otherwise, a nasty competitor of yours will.
On this occasion, the nasty competitor quietly informs you that he has substituted the WIN paper with one with LOSE typed on it. You are not permitted to speak to anyone about this misdeed, nor are you in a position to switch the papers or the hat. How will you avoid losing the contract?
Solution
After you draw one of the papers, swallow it. The client will be forced to check the remaining paper to determine which one you drew. The client will of course see a paper with LOSE typed on it, assume you drew the WIN paper, and give you the contract.
2 - Fork in the Road
You come to a fork in the road. One path leads to riches and happiness, the other to poverty and despair. Standing at the fork in the road there are two consultants; one always lies and the other always tells the truth. You don’t know which consultant tells the truth, and which lies. If you could ask only one question before you start down the path, what question do you ask the consultants?
Solution
Ask either consultant which path the other would say and then take the opposite one. The consultant who lies knows the other will give the correct answer, so will lie and tell you the wrong path. The consultant who tells the truth knows the other will lie, so also tells you the wrong path.
3 - Fox, Goose and a Bag of Beans
Once upon a time a farmer went to market and purchased a fox, a goose, and a bag of beans. On his way home, the farmer came to the bank of a river and hired a boat. But in crossing the river by boat, the farmer could carry only himself and a single one of his purchases - the fox, the goose, or the bag of the beans. If left alone, the fox would eat the goose, and the goose would eat the beans.
The farmer's challenge was to carry himself and his purchases to the far bank of the river, leaving each purchase intact. How did he do it?
Solution
The first step must be to bring the goose across the river, as any other will result in the goose or the beans being eaten. When the farmer returns to the original side, he has the choice of bringing either the fox or the beans across. If he brings the fox across, he must then return to bring the beans over, resulting in the fox eating the goose. If he brings the beans across, he will need to return to get the fox, resulting in the beans being eaten. Here he has a dilemma, solved by bringing the fox (or the beans) over and bringing the goose back. Now he can bring the beans (or the fox) over, leaving the goose, and finally return to fetch the goose.
His actions in the solution are summarised in the following steps:
- Bring goose over
- Return
- Bring fox or beans over
- Bring goose back
- Bring beans or fox over
- Return
- Bring goose over
Thus there are seven crossings, four forward and three back.
4 - Three Light Switches
You are standing outside a training room and have no way of seeing inside. The door is closed and there are three switches on the wall. The switches control three different light bulbs in the training room. Once you open the door, you may never touch the light switches again.
How can you definitively establish which switch is connected to which light bulb?
Solution
Turn on the first two switches. Leave them on for five minutes. Once five minutes has passed, turn off the second switch, leaving one switch on. Now enter the training room. The light that is still on is connected to the first switch. Whichever of the other two is warm to the touch is connected to the second switch. The bulb that is cold is connected to the switch that was never turned on.
5 - Three Boxes
You have been given three boxes of training materials, which are labelled as follows:
[Box 1] Workbooks
[Box 2] Stationery
[Box 3] Workbooks & Stationery
In each case the label is on the wrong box. You must move the labels to the appropriate boxes, but you may only remove a single item from one of the boxes (without looking inside or feeling around). You may not look in the other boxes, nor may you pick them up and shake them, etc.
Can this be done? If so, how?
Solution
Yes, it can be done. You have to start with the box labelled Workbooks & Stationery (which actually contains one or the other). Remove an item from the box, say a workbook, and change the label accordingly. The box labelled Stationery is mislabelled and cannot be Workbooks, so it must be Workbooks & Stationery. And the box that was labelled Workbooks must be Stationery.
In summary:
[Box 1] Workbooks -> Stationery
[Box 2] Stationery -> Workbooks & Stationery
[Box 3] Workbooks & Stationery -> Workbooks
6 - Red & White Wine
A new learning initiative has been very successful and you host a celebration for all the key stakeholders involved.
During the event, one of the participants gets a bit carried away and takes a glass of red wine from one jug and pours it into a jug of white wine, thoroughly mixes it, and then takes a glass of this mixture and pours it back into the red wine jug.
Given that there were equal amounts of red and white wine to start with, is there more red wine in the white wine or is there more white wine in the red wine?
Solution
Neither. The amount of red wine in the jug of white will equal the white wine in the jug of red.
Imagine you have 90ml of both wine to start. You take 10ml of red (leaving 80ml behind) and pour it into the white wine, which you thoroughly mix. You now have a 100ml mixture containing 90ml white and 10ml of red. When you remove 10ml it will contain 9ml of white and 1ml of red wine, leaving behind 81ml of white and 9ml of red. Adding this to the red wine gives you 80ml red + 1ml red + 9ml white, i.e. 81ml red + 9ml white wine.
Of course you could always argue that it doesn’t matter since no one there could work it out and there was none left by the end of the evening!
7 - Four Sporty Facilitators
There are four facilitators: Alice, Ben, Cathy and David. Each likes a different sport, including running and tennis. In addition you know:
(a) Alice and Ben met when one of them won a swimming race.
(b) Cathy and David met when one of them was playing hockey.
(c) Alice is not a swimmer or a runner.
(d) David is a friend of the hockey player’s brother.
Which sport does each facilitator like?
Solution
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Swimming
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Hockey
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Running
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Tennis
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Alice
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x (c)
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x (b)
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x (c)
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â (d)
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Ben
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â (d)
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x (b)
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Cathy
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x (a)
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â(d)
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David
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x (a)
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â (d)
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8 - Two Consultants and a Falcon
Two consultants live 60 km apart with a straight road between them. One day, they leave home at the same time and drive towards each other. Just as they depart, a falcon flies into the air in front of the first car and flies ahead to the second consultant. When the falcon reaches the second consultant, it turns around and flies toward the first consultant. The falcon continues in this way until the consultants meet. Assume that both consultants drive at a constant 60 kph and that the falcon flies at a constant 80 kph. How many kilometres will the falcon have flown when the consultants meet?
Solution
Use the equation: Distance = Speed x Time
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Car A
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Car B
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Falcon
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Distance
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30 km
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30 km
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40 km
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Speed
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60 kph
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60 kph
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80 kph
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Time
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1/2 hour
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1/2 hour
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1/2 hour
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Adapted from a problem by Kenneth A. Kiewra: The Matrix Representation System: Orientation, Research, Theory, and Application, in Raymond P. Perry and John C. Smart (Editors): Effective Teaching in Higher Education: Research and Practice, Agathon Press (May 1997), page 147.
9 – Six Apple Slices
There are six participants at your workshop. When you break for morning tea you find a box containing six apples slices has been supplied. How can you divide them among the participants so that each has one apple slice and one apple slice remains in the box?
Solution
Give five participants one apple slice from the box and give the sixth participant the box containing the last apple slice.
10 – Nine Words in One
You are attending a course on technical writing skills. The facilitator decides to stimulate the group with the following brain teaser:
There is a common English word that is nine letters long. Each time you remove a letter from the word, it remains a valid English word - from nine letters right down to a single letter.
What is the original word, and what are the eight words that it becomes by removing one letter at a time?
HINT: S _ _ _ _ _ _ _ G
Solution
The base word is Startling. Removing one letter at a time, the eight words are: Starting (or Starling), Staring, String, Sting, Sing, Sin, In, I.
11 – How Old is Alec?
Alec is a new trainee and Bob is his coach.
Bob is 50 years old, which is 4 years older than twice Alec’s age. How old is Alec?
Solution
Let Alec's age = x.
Then twice Alec's age is 2x, and 4 years older than twice Alec's age is 4 + 2x.
Hence: 50 = 4 + 2x.
Subtracting 4 from each side we get: 46 = 2x.
And dividing both sides by 2 gives: 23 = x.
So Alec is 23 years old.
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