Arrange 7 marbles on a flat desk so that there are 6 lines of 3 marbles each. via youtube Solution video can be found here.
Monthly Archives for June, 2013
Consider the 7x7 grid shown below: Each cell must be filled in with an integer from 1 to 7 that represents the height of the building. The numbers given at the sides (top, bottom, left, right) represent how many buildings are visible when seen from that location. A taller building blocks the view of all shorter buildings behind it. Also, … Continue reading the story "Skyscrapper puzzle"
The Peg Solitaire puzzle is also known as Conway's Soldiers Puzzle. It consists of a checkerboard that extends infinitely, a horizontal dividing line, and an arbitrary number of pegs (soldiers) below the horizontal line. See the figure below: A move consists of one peg jumping over another adjacent peg into an empty cell either vertically or horizontally, but not diagonally. … Continue reading the story "Peg Solitaire Puzzle"
Let f(t,n) denote the maximum number of connected regions into which an n-dimensional space can be divided using t hyperplanes that are (n-1)-dimensional. Assume t>=n. We solved for f(t,2) here and f(t,3) here . Find a recursive relation for f(t,n). Are you surprised that the answer f(t,n) is the same as the one you obtained in the egg dropping experiment posted … Continue reading the story "Dividing an n-dimensional space using (n-1)-dimensional hyperplanes"
Suppose you have n eggs and a maximum of t tries for the egg drop experiment from yesterday (found here). Let f(t,n) be the maximum number of floors for which it is possible to compute the egg-breaking floor. Find a recursive relation to compute f(t,n). - via Wikipedia.
Suppose you have 3 identical sturdy eggs. You are living in a 100 floor building. You like to know the smallest floor from which an egg will break when dropped. However it is time consuming to keep going to each floor for a trial. You want to minimize the worst case number of trials. So you don't want to go from the bottom floor to … Continue reading the story "Egg drop experiment"
What is the maximum number of regions into which 3-d space can be split using n planes? For example, n=1 plane creates 2 regions, n=2 planes creates 4 regions in space, etc. Refer to yesterday's puzzle here for an easier version.
What is the largest number of regions into which n lines can divide a plane? For example, 1 line creates 2 regions, 2 lines creates 4 regions, 3 lines creates 7 regions, etc. -- via discussions in Thomas Cover's puzzle meetings.
A boat carrying a stone is floating in a swimming pool. What would happen to the level of water in the pool if you take the stone from the boat and throw it into the pool? via Math exchange
Suppose you have a rectangle of dimensions N x 2. (length: N, Width: 2). How many circles of diameter 1 can be embedded in this rectangle so that the circles are non-intersecting? via stack exchange