Search results

This is the only one I can't figure out. I spent a good half hour on it, but it doesn't lend itself to any tricks I've seen before (it's not linear recursive, so I can't write down a linear operator and diagonalise it, it doesn't become more tractable if I write down (x_n) in terms of (x_{n-2})...

Those ones are pretty standard high school math competition questions. Some of the later ones in the thread are more interesting.

Easy enough. It's the volume of an n-dimensional right polyhedron with height is 1 and whose base is the (n-1)th dimensional polyhedron which solved the problem for n-1. The forms are: a line, an isosceles right triangle of base/height 1, a right pyramid with the previous isosceles right...

The answer is 10. Label the bottles 0,1,2,...999 Line the 10 people up in a row. They are going to act like digits of a binary number. Pour a bit of bottle X in the glass of each of the people for whom the binary representation of X sets their digit to 1. Repeat for all X. In other words...

The answers to 2 and 4 are incorrect. 5 is an ill-posed question. Edit: there is a possibility that the answer to two is merely a typo. If you insert an i after the \(\sqrt{3}\) then it becomes correct. The real question is why you would put it in a+ib notation instead of exponential notation...