3. A man wanted to enter an exclusive club but did not know the password that was required. He waited by the door and listened. A club member knocked on the door and the doorman said, "twelve." The member replied, "six" and was let in. A second member came to the door and the doorman said, "six." The member replied, "three" and was let in. The man thought he had heard enough and walked up to the door. The doorman said, "ten" and the man replied, "five". But he was not let in. What should have he said?

4. There are 20 pieces of bread to divide among 20 people. A man eats 3 pieces, woman eats 2 pieces and a child eats half piece of bread. Tell the correct combination of men, women and children so that they are 20 people in total and everyone gets the bread. Note that a man cannot eat less than 3 or more than 3. A woman cannot eat less than 2 or more than 2 and the child cannot eat less than half or more than half piece of the bread. You have to tell there are how may are men, women and children in those 20 people.

5. A cube of side 4cm is painted with 3 colors red, blue and green in such a way that opposite sides are painted in the same color. This cube is now cut into 64 cubes of equal size.

- How many have at least two sides painted in different colors.
- How many cubes have only one side painted.
- How many cubes have no side painted.
- How many have exactly one side not painted.

7. Three people picked 65 apples altogether. At the first tree they each picked the same number of apples. At the second tree they each picked 3 times as many as they picked at the first tree. When they finished at the third tree, the group had 5 times as many apples as they had when they started at that tree. At the fourth tree the group picked just 5 apples. How many apples did each person pick at the first tree?

8. 4 criminals are caught and are to be punished. The Judge allows them to be freed if they can solve a puzzle. If they do not, they will be hung. They agreed. The 4 criminals are lined up on some steps (shown in picture). They are all facing in the same direction. A wall seperates the fourth man from the other three.

- Man 1 can see men 2 and 3.
- Man 2 can see man 3.
- Man 3 can see none of the others.
- Man 4 can see none of the others.

- They are not allowed to turn round or move.
- They are not allowed to talk to each other.
- They are not allowed to take their hats off.

9. At a party, everyone shook hands with everybody else. There were 66 handshakes. How many people were at the party?

10. You have to measure exactly 4 liters of water, but you only have a 3-liter bottle and a 5-liter bottle. How do you do it?

1. Consider the trade-story as if it describes two separate trades, where: In the first trade, the man buys something for $60 and sells it again for $70, so he makes a profit of $10. In the second trade, the man buys something for $80 and sells it again for $90, so he makes again a profit of $10.

Conclusion: The man makes an overall profit of $10 + $10 = $20.

You can also look at the problem as follows:

The total expenses are $60 + $80 = $140 and the total earnings are $70 + $90 = $160. The overall profit is therefore $160 - $140 = $20.

2. 100 Km/hr because that is the top speed of the bus.

3. The man had to reply the number of characters in the word the Doorman was asking. He should have replied "Three" instead of "Five".

4. There are 5 women, 1 man and 14 children.

5. Here are the answers.

- Cubes that have at least two sides painted in different colours are 24 + 8 = 32.
- Cubes that have only one side painted are 24.
- Cubes that have no side painted = 8.
- Cubes that have exactly one side not painted = 0.

6. There are actually 204 squares on a chessboard. Surprised! Here is the explanation. There are 64 (1x1) squares. There are 49 (2x2) squares. There are 36 (3x3) squares. There are 25 (4x4) squares. There are 16 (5x5) squares. There are 9 (6x6) squares. Then there are 4 (7x7) squares and 1 big 8x8 square. So, there are a total of 204 squares on a normal chessboard.

7. One Apple8. Man 1 will shout first. If Man1 will not shout then Man 2 surely shouts.

Reason: Man 1 can see the other two criminals? hats. If the hats are same color then he told his hat is opposite color of remaining two hats. So he shouts first. If Man 1 does not shout, it means that the hats of Man 2 and Man 3 are of different color. So Man 2 sees the color of Man 3 hat and he tells that the color of his hat is opposite to the color of Man 3 Hat.

9. With two people, there is one handshake. With three people, there are three handshakes. With four people, there are six handshakes. In general, with n+1 people, the number of handshakes is the sum of the first n consecutive numbers: 1+2+3+...+n. Since this sum is n(n+1)/2, we need to solve the equation n(n+1)/2 = 66. This is the quadratic equation n

^{2}+n-132 = 0. Solving for n, we obtain 11 as the answer and deduce that there were 12 people at the party.

10. Fill the 3-litre bottle and pour it into the empty 5-litre bottle. Fill the 3-litre bottle again, and pour enough to fill 5-litre bottle. This leaves exactly 1 litre in the 3-litre bottle. Empty the 5-litre bottle; pour the remaining 1 litre from the 3-litre bottle into the 5-litre bottle. Fill the 3-litre bottle and pour it into the 5-litre bottle. The 5-litre bottle now has exactly 4 litres.

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