In the following puzzle an example on multiplication is encrypted with the letters of Latin alphabet: \[{BAN}\times {G}= {BOOO}.\] Different letters correspond to different digits, identical letters correspond to identical digits. The task is to solve the puzzle.
The edges of a cube are assigned with integer values. For each vertex we look at the numbers corresponding to the three edges coming from this vertex and add them up. In case we get 8 equal results we call such cube “cute”. Are there any “cute” cubes with the following numbers corresponding to the edges:
(a) \(1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12\);
(b) \(-6, -5, -4, -3, -2, -1, 1, 2, 3, 4, 5, 6\)?
There are 36 checkers on a \(6\times6\) board (one checker per one cell). They are numbered from 1 to 36. You need to rearrange the checkers so that the ones with numbers which differ by 1 are neighbours (their cells share an edge) and additionally all square numbers have to correspond to the checkers of one (a) horizontal line; (b) of the diagonals. Is it possible or not?
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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?