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:

1. 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.
2. The quantity of oil in the vinegar container is greater than the quantity of vinegar in the oil container.
3. The quantity of oil in the vinegar container is the same as the quantity of vinegar in the oil container.
4. The quantity of oil in the vinegar container is the less than the quantity of vinegar in the oil container.
5. 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.
6. 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.

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:

1. Z = X + i Y in X and Y coordinates.
2. Z = R [Cos(ß) + i Sin(ß)] where R is the modulus and ß is the angle in vector form.
3. Z = e(A + i ß) = eA * e(i ß) where eA = 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.