**1.) Jolly Jugs Problem**

You are standing next to a well, and you have two jugs. One jug has a content of 3 liters and the other one has a content of 5 liters.

** Question: **How can you get just 4 liters of water using only these two jugs?

### Solution

Fill the 5 liter jug. Then fill the 3 liter jug to the top with water from the 5 liter jug. Now you have 2 liters of water in the 5 liter jug. Dump out the 3 liter jug and pour what’s in the 5 liter jug into the 3 liter jug. Then refill the 5 liter jug, and fill up the 3 liter jug to the top. Since there were already 2 liters of water in the 3 liter jug, 1 liter is removed from the 5 liter jug, leaving 4 liters of water in the 5 liter jug.

**2.) Growing Water-Lily Problem **

In the middle of a round pool lies a beautiful water-lily. The water-lily doubles in size every day. After exactly 20 days the complete pool will be covered by the lily.

**Question:** After how many days will half of the pool be covered by the water-lily?

### Solution

Because the water-lily doubles its size every day and the complete pool is covered after 20 days, half of the pool will be covered one day before that, after 19 days.

Conclusion: After 19 days half of the pool will be covered by the water-lily

**3.) The Wolf, the Goat, and the Cabbage Problem**

A man has a wolf, a goat, and a cabbage. He must cross a river with the two animals and the cabbage. There is a small rowing-boat, in which he can take only one thing with him at a time. If, however, the wolf and the goat are left alone, the wolf will eat the goat. If the goat and the cabbage are left alone, the goat will eat the cabbage.

**Question:** How can the man get across the river with the two animals and the cabbage?

### Solution

First, the man takes the goat across, leaving the wolf with the cabbage. Then he goes back. Next, he takes the wolf across. Then the man goes back, taking the goat with him. After this, he takes the cabbage across. Then he goes back again, leaving the wolf with the cabbage. Finally, he takes the goat across.

First, the man takes the goat across, leaving the wolf with the cabbage. Then he goes back. Next, he takes the cabbage across. Then the man goes back, taking the goat with him. After this, he takes the wolf across. Then he goes back again, leaving the wolf with the cabbage. Finally, he takes the goat across.

**4.) Happy Handshaking Problem**

Jack and his wife went to a party where four other married couples were present. Every person shook hands with everyone he or she was not acquainted with. When the handshaking was over, Jack asked everyone, including his own wife, how many hands they shook. To his surprise, Jack got nine different answers.

**Question:** How many hands did Jack’s wife shake?

### Solution

Because, obviously, no person shook hands with his or her partner, nobody shook hands with more than eight other people. And since nine people shook hands with different numbers of people, these numbers must be 0, 1, 2, 3, 4, 5, 6, 7, and 8.

The person who shook 8 hands only did not shake hands with his or her partner, and must therefore be married to the person who shook 0 hands.

The person who shook 7 hands, shook hands with all people who also shook hands with the person who shook 8 hands (so in total at least 2 handshakes per person), except for his or her partner. So this person must be married to the person who shook 1 hand.

The person who shook 6 hands, shook hands with all people who also shook hands with the persons who shook 8 and 7 hands (so in total at least 3 handshakes per person), except for his or her partner. So this person must be married to the person who shook 2 hands.

The person who shook 5 hands, shook hands with all people who also shook hands with the persons who shook 8, 7, and 6 hands (so in total at least 4 handshakes per person), except for his or her partner. So this person must be married to the person who shook 3 hands.

The only person left, is the one who shook 4 hands, and which must be Jack’s wife. The answer is: Jack’s wife shook 4 hands.

**5.) The Round Table Problem **

Yesterday evening, Helen and her husband invited their neighbours (two couples) for a dinner at home. The six of them sat at a round table. Helen tells you the following: “Victor sat on the left of the woman who sat on the left of the man who sat on the left of Anna. Esther sat on the left of the man who sat on the left of the woman who sat on the left of the man who sat on the left of the woman who sat on the left of my husband. Jim sat on the left of the woman who sat on the left of Roger. I did not sit beside my husband.”

**Question:** What is the name of Helen’s husband?

### Solution

From the second statement, we know that the six people sat at the table in the following way (clockwise and starting with

Helen’s husband): Helen’s husband, woman, man, woman, man, Esther

Because Helen did not sit beside her husband, the situation must be as follows: Helen’s husband, woman, man, Helen, man, Esther

The remaining woman must be Anna, and combining this with the first statement, we arrive at the following situation: Helen’s husband, Anna, man, Helen, Victor, Esther

Because of the third statement, Jim and Roger can be placed in only one way, and we now know the complete order:Helen’s husband Roger, Anna, Jim, Helen, Victor, Esther

Conclusion: the name of Helen’s husband is Roger.