Five identical regular hexagons are inscribed without overlap inside a regular hexagon of side length 1.The sides of length s of the five identical hexagons is the largest possible. Find s.
I am a 370 17250.
To find out what it means, solve :
--A WISHFUL PUZZLE!
Here is pi to 37 decimal places.
It turns out that 31415926535897932384626433832795028841 is prime, but you would need a computer to figure that out. Here is e to 37 decimal places.
The largest prime number that is a substring of these digits is 828182845904523536028747135266249. Of course, that would be hard to find without a computer. However, if I showed you the first 37 digits after the decimal point of (sqrt(3)-1)^(sqrt(2)-1), then you could easily find the largest prime number in those digits. You could do it in your head. How? What is the largest prime substring of the first 37 digits of (sqrt(3)-1)^(sqrt(2)-1)?
Using three colors, can one color every point in 3D-space, so there is no cuboid with same-colored corners?
Let [x] denote the closest integer to x.
Find the last 5 digits of [100000!/e]
For some real-valued functions, the graph has a center of symmetry. For example, for cubic polynomials, this is the inflection point.
We call a function super symmetric, when it is defined for all real numbers and its graph has more than one center of symmetry. Sine and Cosine are examples.
Show that every super symmetric function is the sum of a linear function and a periodic function.