1st Puzzle:

You have two large containers of different size, one is 3 times larger than the other one, and the larger one is nearly full of pure oil, the other one is nearly full of pure vinegar.

You dip a ladle into the oil container and draw an exact ladleful of oil which you now pour into the vinegar container.

You unevenly stir the vinegar+oil container then you dip the same ladle into this container and you draw an exact ladleful of the mixture which you now pour into the oil container.

Bearing in mind the size of the containers, the very small size of the ladle, the fact that oil and vinegar are not miscible and the stirring action mixed the 2 products unevenly in any case, which of the 6 statements below is correct:

- With the information given it is impossible to say for certain whether the quantity of oil remaining in the vinegar container is larger, equal or smaller than the quantity of vinegar remaining in the oil container.
- The quantity of oil in the vinegar container is greater than the quantity of vinegar in the oil container.
- The quantity of oil in the vinegar container is the same as the quantity of vinegar in the oil container.
- The quantity of oil in the vinegar container is the less than the quantity of vinegar in the oil container.
- The quantity of oil in the vinegar container is PROBABLY greater than the quantity of vinegar in the oil container, but there is a small probability that it is either the same or smaller.
- The quantity of oil in the vinegar container is PROBABLY smaller than the quantity of vinegar in the oil container, but there is a small probability that it is either the same or greater.

To find what the correct answer is, click the Answer word

2nd Puzzle:

The answer to the following problem can be obtained rapidly by making
cunning use of the lack of information.

A sphere, originally solid, has been drilled along one axis by a
standard cylindrical drill. The remaining part measures exactly 6 cm
across flats.

What is the volume of the remaining part ?

Can you prove it ?

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3rd Puzzle:

You and a friend observe a room full of about 40 strangers. Neither
you nor your friend know anyone, yet your friend is prepared to bet
$10.00 that at least two people in the room have a birthday falling
on the same day of the year and he is prepared to offer you 3 to 1
odds. Based on your knowledge of statistics, should you accept the
challenge?

What is the probability that your friend will win ?

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4th Puzzle:

An explorer decides to test his latest acquisition, a new fangled GPS
with bells and whistles which, using 24 satellites, reports his location
on earth to within a few meters . To test it he walks South for 15 km.
At this point he suddenly sees a bear and decides wisely to move in a
different direction hence he now walks West for 15 km. He then walks
North for 15 km and, amazingly, finds himself where he started from
originally.

What is the colour of the bear?

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5th Puzzle:

The same explorer as in puzzle 4 has now moved to a far away continent
where he knows bears don't exist. Still not satisfied that his GPS is
working correctly (despite the serviceman's assurance that it is), he
repeats the test (eg South for 15 km, then West for 15 km, then North
for 15 km) and, amazingly, finds himself again where originally he
started from. The only living creature which he has ever seen on this
continent is a large bird, the male of the species seemingly spending
a lot of time trying to hatch the egg laid by the female by holding the
egg between the top of its feet and its lower abdomen.

What is the name of the bird species?

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6th Puzzle:

Complex numbers are important to both electrical and process control
engineers. Therefore you have no excuse for not solving this puzzle
(unless you are unlucky enough not to belong to our elite category).

A complex number,Z , can be expressed in several ways:

- Z = X + i Y in X and Y coordinates.
- Z = R [Cos(ß) + i Sin(ß)] where R is the modulus and ß is the angle in vector form.
- Z = e
^{(A + i ß)}= e^{A}* e^{(i ß)}where e^{A}= R and ß is defined above.

Based on the above reminders, calculate the **imaginary root
of the imaginary number**.

Clue: remember that extracting a root is the same as raising to the
inverse of the power (e.g. square root = power 1/2, cubic root = power
1/3 etc...)

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7th Puzzle:

You have a chess board, and a set of dominoes. The dominoes are of such
size that they cover exactly 2 squares of the chess board. Obviously
since there are 64 squares on the chess board, you can cover it fully
with 32 dominoes.

You cut off two diagonally opposite squares on the chess board so
that only 62 squares are left. How many dominoes can you fit on the
board such that each dominoe covers exactly 2 squares? Dominoes
overlapping each other and dominoes sticking out are not allowed.

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8th Puzzle:

A school has exactly 100 students and one hundred lockers. The first
student who enters the school opens all the locker doors. The second
student enters and shuts every second door. The third student enters
and toggles every third door (ie if it is shut he opens it, and if it is
open he shuts it). The fourth student enters and toggles every fourth
door. And so on until all 100 students have passed through.

What is the state of the doors after the 100th student has passed
through?

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9th Puzzle:

You are a contestant on a TV game show and the presenter points to 3
doors and tells you that behind one of the doors is a car. He asks you
to choose a door and that if you choose the door behind which the car
is, the car is yours. So you pick a door and tell him which is your
choice. The presenter then opens one of the other two doors, revealing
that there is nothing behind it, and now, to make the suspense last
longer, offers you the possibility of changing your original choice.
What should you do to maximise the likelyhood of winning the car?

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Answer word