Suppose the positive integer n is odd. First Sam writes the numbers 1,2, \ldots, 2 n on the blackboard. Then he picks any two numbers a, b, erases them, and writes, instead, |a-b| . Prove that an odd number will remain at the end.
Show that five lattice points can always be connected in a specific way.
Prove that a certain number can never be prime.
Dive into the world of Euler’s phi-function and reveal its hidden connection to prime factors
Here, in a figure of 9 points and 8 straight lines, two additional straight lines are to be obtained by relocating two points. Can you do that?
This puzzle is about figuring out angles in triangles.
How many cuts does he need to cut a wooden cube into pieces?
