/puzzle/ - Puzzles and recreational math

Find the next two numbers in the sequence

1, 2, 3, 5, 11, 31, ?, ?

>>64

similarly:

6, 2, 5, 5, 4, 5, 6, 3, ?, ?

>>73

Excuse me if I'm missing some commonly known function (or lack thereof) with these tools, but if you can get a right angle from the drafting triangle, couldn't you just draw a square around the circle and then connect opposite corners to get the center?

>>74

I don't think so, at least not in that straightforward way. You'd have to make sure the legs of the triangle are tangents to the circle without a compass.

Imagine an infinite Euclidean plane. On four lines in general position (no two parallel, no three meet at the same point), a dot is, always has been, and always will be moving at constant velocity along the line. Numbering the lines and dots 1-4, we know that dot 1 and 2 meet all the other dots eventually, What can we say about whether dot 3 and 4 meet? What about the positions of the dots at an arbitrary time?

A cart with a tank of water in it is on a flat surface under Earth-equivalent gravity. (9.81 m*s^-2). It is accelerating along the surface at a constant rate. The water level in the tank is tilted 35 degrees off of horizontal. What is the magnitude of the acceleration?

You have 6 bags and 31 doo-dads. Arrange it so that each bag has an odd number of doo-dads in it.