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A squint man has a visual deflection of 30 degrees. This means that there is a 30 degrees angle between the direction that he sees as straight and the direction that he walks in. How long is the path of his walk when he can see that he is walking straight towards a pole that was 100 metres away from him at the beginning?
Note: It is possible (and the preferred way, actually) to solve this puzzle without using integral calculus.
You have eight almost identical balls, but one of them is a little bit lighter than the others. It is not that lighter, though, that you can tell the difference by hand, but you have a two-armed balance. How can you find the light ball with only two measures?
Given a square of NxN fields, some of the fields are initially painted to black while the other fields are left empty. Then the table begins its life: every empty field that has at least two black neighbours (by the four edges) is painted to black automatically. Obviously, the full table can be auto-painted if it is allowed to use enough initial fields. It is just one thought further to see that N initial fields are enough for this (e.g. a diagonal of the square is painted initially).
Prove that less than N initial fields are not enough to auto-paint the full table. Try to find an elegant (i.e. short) solution.
The wanderer arrives at a fork in the road taken care of by two guards. One of the two possible branches leads to life while the other one means death. One of the guards always tells the truth but the other guard always lies. Apart from this, the two guards are identical, they even look the same, so that it is not known which one is the liar. The guards know each other and they know which branch means life and which one means death.
How can the wanderer determine, with only one yes/no question, which road leads to life?
Peter and Paul are twins and they haven't got any other brothers or sisters. One day Peter celebrated his birthday. Two days later Paul, Peter's elder brother, celebrated his birthday. How come? |
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