How many times a day do a clock’s hands overlap?
How do you cut a rectangular cake into two equal pieces when someone has already removed a rectangular piece from it? The removed piece can be of any size or orientation. You are allowed just one straight cut.
Why does a mirror reverse right and left instead of up and down?
Max asked Emily how old she was. She replied that she was 13 years old the day before yesterday, and will be 16 next year. Then, Max asked her brother, whether it was true, and he said yes. How is it possible if nobody was lying?
Place coins on a \(6\times 6\) chequered board (one coin on one square), so that all the horizontal lines contain different number of coins, and all vertical lines contain the same number of coins.
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?