BMAD

How many spin-able numbers are there from 0 to 99999 ? This is a no-computer puzzle, only right answers with explanation will be accepted. nevermind

Five people (A,B,C,D,E) each need to complete one task (1,2,3,4,5). The amount of money each person would need to complete each tasks is reported in the matrix below. 1 2 3 4 5 +---------- A | 8 3 5 4 3 B | 2 6 9 4 7 C | 6 1 8 4 3 D | 5 7 9 8 8 E | 5 7 9 4 3 As the assigning manager, who should do which task?

100%??

You enter a room with two chests. You know that one chest has a lot of money (but you are unsure as to which). You know the other chest has half as much. Being the greedy person you are you want the most money but the chest are indistinguishable from each other outside of opening and counting the contents. You picked the first chest. Just before you open it, the owner of the chests offers you an opportunity to switch. Should you?

Pretend you have a rectangle that is divided into two smaller rectangles where the area of one rectangle is twice that of the other rectangle. If you were to pick a point at random inside the rectangle, what is the probability that the point is within the larger rectangle?

Not until you have raised the question. Clearly their must be an upper bound and lower bound between which the area could exist.

my mistake. I did mean to state symmetry. well done!

Suppose we have two congruent equilateral triangles with side length of 8ft. They are on top of each other in the same orientation. Now One triangle is rotated by 180 degrees and is laying on top the other triangle forming a star. The triangles are positioned relative to each other such that the distance from the base of one triangle is 6ft to the base of the other triangle. What is the area of the star?

Assume an exclusive OR.

Why can't a right triangle with an hypotenuse of sqrt(24) have an area of 13 squared inches?

There is an equilateral pentacontagon (a polygon with 50 sides). In one of its vertex stands Dr. Faust. He has three options 1) walk to the diametrically opposed point free of charge; 2) walk counterclockwise to the neighboring vertex by paying $1.05 to Mephistopheles; 3) walk clockwise to the neighboring vertex by receiving a payment of $1.05 from Mephistopheles. If it is given that Dr. Faust has been everywhere at least once, prove that at some point someone paid no less than $25.

Let’s say there is a gathering where among any three people there are two friends. Is it true that people at such gathering can always be divided into two groups in a way that every two people in one group are friends?

Let me see if i can ask my question better. Suppose you have twelve rods of two different sizes. One size is 4 in. The other is 8 in. There are 8 - 4in. Rods and 4 - 8 in rods. Use the 4 in rods to construct two squares. Stand your squares up perpendicular to your table and parallel to each other. Now take one 8 in rod and connect it to the top left of one square (first square) and bottom left of the other. Take your second rod, connect it to the top right of the first square and top left of the other. Third rod, bottom right of first and top right of second. Connect the last rod to the remaining vertices. All rods will remain straight through this process. Find the volume and compare it to the volume of 4x4x8

The square faces are the front and back. If you think of the congruent squares each having vertices abcd in the same clockwise rotation each resting parallel to the other. Then connect 8 inch edges in the following manner, front A to back B, front B to back C, front C to back D, and front D to back A. How does this volume compare to a standard rectangular prism of 4x4x8?

And?