A young and ambitious software engineer is working on his own basic version of an intelligent personal assistant. The application can only answer closed questions (a closed question is a question that can be answered only ‘yes’ or ‘no’). He installs this application on three mobile devices and runs a set of tests. He discovers there is one unstable device. From time to time the application gives wrong answers, but you cannot really predict when. Being exhausted after unsuccessful attempts to find the mistake in his code, the software engineer goes to sleep. The next morning he cannot remember which device is not working properly. Taking into account that devices are connected to the same server (so normally working applications can detect which one is not always receiving the signal) explain how in two questions the engineer can determine the unstable device. One question is for one device only.
A pencil box contains pencils of different colours and different lengths. Show that it is possible to choose two pencils of both different colours and different lengths.
Could you formulate a question which both a liar and a knight would answer identically (either “Yes” or “No”)?
Inhabitant A tells Inhabitant B, “At least one of us is a liar”. Who is A and who is B?
Three inhabitants are passing by. You ask the three inhabitants, “How many among you are knights?” The first one replies, “There is none”. The second inhabitant argues, “There is only one”. What should the third inhabitant say?
John is a knight, he never lies. But when you ask him the same question twice, his second answer suddenly is different from the first. How is it possible?
a) Twelve inhabitants are sitting under a big tree. One of them says, “There is at least one liar among us”. How many knights can be among them?
b) A different group of other twelve inhabitants is resting by the river. Suddenly, one of them exclaims, “If everyone except me is a liar, then I am a liar too”. How many liars can be among them?
Ten inhabitants are sitting around the table. Each one of them says, “My neighbour on the right is a knight”. How many knights and liars are sitting there?
lbert (A), his wife Beatrix (B), and their children Charlie (C), Dan (D) and Elizabeth (E) live in a bungalow. They have a really nice TV set. It is known that
1) If A is watching the TV, then B is watching the TV.
2) At least one of D and E is watching the TV.
3) Only one of B and C is watching the TV.
4) Either C and D are watching the TV together, or both are not watching.
5) If E is watching the TV, then both A and D are also watching the TV. Can you tell who is watching the TV in this family and who is not?
Once I found a really strange notebook. There were 100 statements in the notebook, namely
“There is exactly one false statement in this notebook.”
“There are exactly two false statements in this notebook.”
“There are exactly three false statements in this notebook.”
...
“There are exactly one hundred false statements in this notebooks.”
Are there any true statements in this notebook? If there are some true statements, then which ones are true?