Excel in math, science, and engineering
Let \(x\leq y \leq z\) be positive integers satisfying \(x^y + y^z = z^x\).
Find the sum of all possible values of \(v = x+y+z\).
A line segment of length 2 moves in the \(xy\)-plane such that it always touches both the coordinate axes. Find the area of the region swept out by the ...
How many pairs of positive integers \((x,y)\) that satisfy the equation
Here is a dodecahedral calendar:
It has got twelve pentagonal faces, like in this animation:
Is it possible to place the months of the dodecahedral calendar in a ...
Alice and Bob play the following game.
A fair coin is tossed repeatedly until we get a consecutive HH or a HT.
Alice wins if it shows a HH.