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

## Skyscrapper puzzle

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"## Peg Solitaire 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"## Dividing an n-dimensional space using (n-1)-dimensional hyperplanes

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"## Egg drop experiment continued

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.

## Egg drop experiment

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"## Dividing space using planes

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.

## Stone in a boat

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

## Number of circles in a rectangle

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