From Puzzles to Programming

Three  persons of different length were in a line. The tallest stood in the back and the shortest stood in front. You have 5 hats of which 3 were black and 2 were white. You put 3 hats randomly on the heads of these persons in a way that none of them knew the color of his hat. You asked the tallest if he could know the color of his hat but he could not. You asked the middle if he could tell the color of his hat but he could not. Then you asked the shortest if he can tell the color of the hat on his head and he answered it is black. How did the shortest know the color of his hat?

Answer

When you asked the tallest about the color of his hat he looked to the 2 hats on the heads in front of him. If these were 2 white hats then definitely the hat on his head would be black as no more white hats were left. This makes the choice of the hats in front of him either 2 black hats or one black hat and one white hat.

Now the middle person is left with three choices i.e. 1) black hats on both his head and the front man's head or 2) a white hat on his head and a black hat on the front man's head or 3) a black hat on his head and a white hat on the front man's head. He could not tell the color of his hat meaning that he saw a black hat on the head of the shortest man standing in front of him and this makes his hat either black or white (choices 1 or 2). From this interpretation, the shortest knew that his hat was for sure black.

Consider a wooden box and a metallic box. Only one of them contain a treasure. On the wooden box a text says: "This box is empty". On the metallic box, a second text says: "Only one of the texts is true". Based on these texts, which box contain the treasure?

Answer

There are 3 possibilities:

A- Both texts are true.

B- The first text is true and the second text is false.

C- The first text is false and the second text is true.

Now, assume possibility 'A'. This means that the second text is true. But this text says that only one of the texts is true which contradicts 'A'.

Assume then possibility 'B'. This means that the first text is true and the second text is false. But this leaves the first text as the only true text making the second print text true thus leading to contradiction to 'B'.

This leaves possibility 'C'. This means that the first print is wrong. In other words it does not hold. Conclusion: The wooden box is not empty and it contains the treasure.

Answer

The minister will say: "I will marry the older sister". If this statement is true then he has to marry the young sister but then this makes his statement false which is contradiction. If his statement is false then he has to marry the older sister, but this makes his statement true which is also a contradiction. In other words, the minister escaped the planned marriage and the king has to wait for another man to knock his door.

You have a lamp inside a room with 3 switches outside the room. Only one switch turn the lamp on. How to find this switch if you are allowed to enter the room only one time and knowing that the light of the lamp cannot be seen from outside.

Answer

Make sure that all the switches are off. Then turn the first switch for a moment then put it off and turn on the second switch. Now enter the room. If the light is on then the second switch is the one that turned the lamp on. If the lamp is still off, then touch the lamp. If it is hot then it is the first switch else it is the third switch that turns the lamp on

A farmer owns a wild dog, a sheep, and hey. He is on the village side of a river. He wants to cross to the other side of this river where he can sell his stuff in the city. He can use a boat which has a space for only 2 items including the farmer himself. In other way, he can carry on the boat either the dog, the sheep or the hey only one at a time. How can he cross the river if we knew that the wild dog will attack the sheep, and the sheep can eat the hey if they were left unattended?

Answer

We know that if the farmer carried the hey first, then the dog might attack the sheep. Also, if he carried the dog, then the sheep might eat the grass/hey. Definitely, he has to carry the sheep first. Once, he moves the sheep to the other side, he moves his boat back where he left the dog and the hey. He carries now the dog and crosses again to the other side and picks the sheep (so that it wouldn’t be attacked) back to the side of the village where he left the hey. Now, he carries the hey and goes to the city side where he has left the dog. He goes in another step to carry back the sheep. All his items are now on the city side of the river.

You have a magnetized bar and an iron bar. Both are identical in shape and size. How would you distinguish between them using no extra materials?

Answer

The magnet bar has 2 attracting poles while its middle-portion has negligible magnetic attraction. If you place the end of one of the bars (call it bar I) at a right angle on the middle point of the other bar (bar II) then there are 2 possibilities: a. Attraction meaning that bar I is the magnetized bar or b. No or minimal attraction meaning that bar I is the iron bar.

 You have 7 choclate cakes and one doughnut lined in a circle. Start clockwise from any cake you pick randomly and eat every 8th cake. Continue counting clockwise again starting from the next remaining cake and eating the 8th cake. What is the sequence of eating the cakes so that you will eat the doughnut last?

Answer:

Number the cakes clockwise.

The sequence of eating the cakes will be: 8, 1, 3, 6, 5, 2, 7, 4

In this sequence, the number 4 is the last and it should correspond to the doughnut. To eat it last then you have to count 4 clockwise from the doughnut and eat the first cake [in this case number 8] and so on.

There are three glasses of capacity- 3, 5, and 8 oz (G1, G2, and G3 respectively). The first two are empty, the last contains 8 oz of water. By pouring water from one glass to another make at least one of them contain exactly 4 oz of water.

Answer

Fill up the 5 oz. glass. Use the 5 oz. glass to fill up the 3 oz. glass. Pour the contents of the 3 oz. glass into the 8 oz. glass. Pour the remaining 2 oz. from the 5 oz. glass into the 3 oz. glass. Fill up the 5 oz. glass from the 8 oz. glass. Use the 5 oz. glass to fill the 3 oz. glass. Using the 1 oz. from the 5 oz. glass leaves the 4 oz. needed:

G1 G2 G3

0  0  8

0  5  3

3  2  3

0  2  6

2  0  6

2  5  1

3  4  1

Another way to solve the puzzle:

G1  G2  G3

0      0     8

3      0     5

0      3     5

3      3     2

1      5     2

1      0     7

0      1     7

3      1     4

Connect the points in the figure below with just 4 lines without moving the pencil out of the paper.

Answer

The trick lies in avoiding to restrict your self to the boundaries made by the points. Actually, the question did not specify how to draw the lines and there will be no solution to the problem if you restrict your consciousness and thus the lines to the boundaries made by the points.