Order Finder

Isaac and Albert were excitedly describing the result of the Third Annual International Science Fair Extravaganza in Sweden. There were three contestants, Louis, Rene, and Johannes. Isaac reported that Louis won the fair, while Rene came in second. Albert, on the other hand, reported that Johannes won the fair, while Louis came in second.

In fact, neither Isaac nor Albert had given a correct report of the results of the science fair. Each of them had given one correct statement and one false statement. What was the actual placing of the three contestants?

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Bulbs

There are three switches downstairs. Each corresponds to one of the three light bulbs in the attic. You can turn the switches on and off and leave them in any position.
How would you identify which switch corresponds to which light bulb, if you are only allowed one trip upstairs?

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Folded sheet of paper

A rectangular sheet of paper is folded so that two diagonally opposite corners come together. If the crease formed is the same length as the longer side of the sheet, what is the ratio of the longer side of the sheet to the shorter side?

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Painted cubes

Twenty-seven identical white cubes are assembled into a single cube, the outside of which is painted black. The cube is then disassembled and the smaller cubes thoroughly shuffled in a bag. A blindfolded man (who cannot feel the paint) reassembles the pieces into a cube. What is the probability that the outside of this cube is completely black?

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semicircle in a circle

Find the area of the largest semicircle that can be inscribed in the unit square.

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Play with four

Using four 4's and any operations, try to write equations that have the numbers from 0 to 100 as the answer.
Example: 49 = 4! * (sqrt 4) + (4/4)

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Where is the missing £1?

Three people check into a hotel. They pay £30 to the manager and go to their room. The manager suddenly remembers that the room rate is £25 and gives £5 to the bellboy to return to the people. On the way to the room the bellboy reasons that £5 would be difficult to share among three people so he pockets £2 and gives £1 to each person. Now each person paid £10 and got back £1. So they paid £9 each, totalling £27. The bellboy has £2, totalling £29. Where is the missing £1?

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Brain Bashers puzzle

Here is snippet of section D of the curious multiple-choice entrance exam into the exclusive Brain Bashers puzzle

Q1. Which is the first question where c) is the correct answer

a) Q3
b) Q4
c) Q1
d) Q2

Q2. Which is the first question where a) is the correct answer

a) Q4
b) Q2
c) Q3
d) Q1

Q3. Which is the first question where d) is the correct answer

a) Q1
b) Q2
c) Q4
d) Q3

Q4. Which is the first question where b) is the correct answer

a) Q2
b) Q4
c) Q3
d) Q1

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Who owns the fish?

There are 5 houses in 5 different colours. In each house lives a person of a different nationality. The 5 owners drink a certain type of beverage, smoke a certain brand of cigar, and keep a certain pet. Using the clues below can you determine who owns the fish?

The Brit lives in a red house.
The Swede keeps dogs as pets.
The Dane drinks tea.
The green house is on the immediate left of the white house.
The green house owner drinks coffee.
The person who smokes Pall Mall rears birds.
The owner of the yellow house smokes Dunhill.
The man living in the house right in the middle drinks milk.
The Norwegian lives in the first house.
The man who smokes Blend lives next door to the one who keeps cats.
The man who keeps horses lives next door to the man who smokes Dunhill.
The owner who smokes Blue Master drinks beer.
The German smokes Prince.
The Norwegian lives next to the blue house.
The man who smokes Blend has a neighbour who drinks water.

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