Difficulty: Advanced

Your friend is thinking of a number among 1, 2, and 3. You can ask him just one question, to which he is allowed to answer only with “yes”, “no”, or “I don’t know”. What would you ask him in order to find his number?

You can ask him the following:

“If I am thinking of a number among 1 and 2, is your number going to be bigger than mine?”

If your friend’s number is 1, he will say “no”. If his number is 2, he will say “I don’t know”. If his number is 3, he will say “yes”.

Can you cut Sam Loyd’s gingerbread dog into two identical pieces?

The solution is shown below.

Ben has a wall clock in his room, but he didn’t wind it one day, so it stopped working. Later that day he left his house, walked to his best friend’s place, who has his own, always precise clock, stayed there for a while, then walked back home. When he arrived, he went to his wall clock and adjusted it to show the correct time. How did Ben do it, if he didn’t see any other clocks during the day, except for the one at his best friend’s place?

Before Ben left his place, he winded his clock. When he went to his friend’s place, he noted for how long he stayed there, say X, and at what time he left, say Y. After Ben got back home, he looked at his own wall clock and calculated the time he was outside, say Z. Then he concluded that the time he was walking was Z – X in total, and therefore it took him (Z – X)/2 time to get from his friend’s place to his own house. He added Y (the time he left his friend’s place) and got Y + (Z – X)/2, the correct time.

These are a few enigmas from the puzzle book CODEX ENIGMATUM. What is the answer to puzzle #9?

• Puzzle #2 After turning the first wheel 22 times to the right, then 19 times to the left, then 15 times to the right, and finally 11 times to the left, the final wheel will spell the word EXIT.
• Puzzle #3 The total number of spots on the hidden sides of the die on the left is 6, which corresponds to the sixth letter in the alphabet – F. Therefore, the four dice on the right correspond to the letters K, I, N, G.
• Puzzle #4 In the mosaic on the right, you can find a little star which contains pieces with letters H, I, D, E.
• Puzzle #6 If you trace the signature on the paper, starting from the large C, you will pass through the letters C, O, N, T, I, N, U, O, U, S.
• Puzzle #8 The picture on the left and the answer to puzzle #6 (“continuous”) suggest that we have to consider the images on the right which can be drawn continuously, without taking off the pencil from the paper or passing through any segment twice. These images are labeled with the letters N, O, S, E.
• Puzzle #9 The first 2 letters from the word NOSE spell NO. The last letter from the word EXIT is T. The first letter from the word HIDE is H. The last three letters from the word KING spell ING. When you combine all of them, you get the word NOTHING.

What number corresponds to 1985?

0 0 0 0 – 4
1 7 5 2 – 0
1 8 7 9 – 3
2 0 6 1 – 2
3 1 4 1 – 0
4 0 9 6 – 3
7 7 7 7 – 0
9 9 7 3 – 2
1 9 8 5 – ???

The numbers on the right count the total number of “holes” in the digits on the left. “1”, “2”, “3”, “4”, “5” and “7” have 0 holes in them. “0”, “6” and “9” have 1 hole in them. “8” has 2 holes in it. Therefore, the corresponding number is 3.

You have to descend a 100-meter vertical cliff. However, you have only a 75-meter long rope and a knife with yourself. On the top of the cliff and halfway down – 50 meters above the ground, there are two big pins stuck in it. How can you get safely down to the ground?

First, you cut the rope at 25 meters and make a loop at the end of the short part. Then you pass the longer part through the loop so that you get a 50-meter long rope (the second 25 meters are doubled). You use this rope to descend to the pin and grab it. Then tie one of the ends of the 50-meter rope to the pin, pull the rest back through the loop and let it fall to the ground.