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Guest Message by DevFuse
 

Perhaps check it again

Member Since 02 Dec 2013
Offline Last Active May 22 2015 05:00 PM
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Topics I've Started

Horizontally randomly moving particle

13 March 2015 - 12:27 AM

<------- g -------  f ------- e ------ d ------ c ------ b ------ A ------- B ------- C ------ D ------- E ------ F ------ G ------>

 

 

A particle originates at point A and can move left one point or move right point for any move.

It cannot be stationary for any move.

 

 

For two moves, the ways can be diagrammed like this:

 

ABC

ABA

Abc

AbA

 

 

Two of those ways begin and end with the particle at the starting point A.

 

 

Question:  For six moves, how many of the ways begin and end with the

particle at the starting point A?

 

 


Maybe factoring a polynomial completely

11 January 2015 - 09:37 PM

Can the following be completely factored over integer coefficients, where the highest degrees

on x and y are both one?

 

 

2x + 3xy - 2y2 - x + 3y - 1

 

 

If not, state that.

 

If so, then show the steps leading up to and the final factored form.


Number of discrete "curves" in two dimensions

14 December 2014 - 08:56 PM

Let n = a positive integer.

 

Suppose you choose n distinct points on a line.  The distance between

any pair of points is irrelevant. 

 

 

A "curve" is either:

 

1) an individual point

 

2) a set of at least two points

 

3) an individual line segment

 

4) a set of at least two line segments

 

5) some combination of the above

 

 

I will label the points with A, B, C, ..., Y, Z, AA, AB, ..., and so on

as needed, consecutively from left to right, as we see them on

the screen.

 

If a line segment contains more than two points (recall that these are

discrete), then they will be labeled with only their endpoints.  Each

"curve" in a list will be separated by a comma.  The ordering in the

list is irrelevant.

 

The topic in this post involves the unordered listing and number of

the total of discrete "curves" in two dimensions for n distinct points,

where n is greater than or equal to one.

 

 

Examples:

--------------

 

 

n = 1

 

 

<----------------- A ---------------->

 

 

List:  {A}

 

Total:  1

 

- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

 

 

n = 2

 

 

<-------------- A ----------- B ------------->

 

 

List:  {A}, {B}, {A, B}, {AB}

 

Total:  4

 

 

Note:  Here, you cannot have {A, AB}, {B, AB}, or {A, B, AB},

because neither point A nor point B is isolated once you

identify AB as a line segment in the set.

 

 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

 

 

n = 3

 

 

<-------- A -------- B -------------- C ----------->

 

 

List of points only:  {A}, {B}, {C}, {A, B}, {A, C}, {B, C}, {A, B, C}

 

List of line segments only: {AB}, {BC}, {AC}

 

List of points and line segments mixed:  {A, BC}, {AB, C}

 

Total:  12

 

 

Note:  Here, you cannot have {B, AC}, because point B is not

an isolated point.  It is part of line segment AC, and AC has

already been listed.

 

- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

 

 

Puzzle:  Compute the total number of "curves" for n = 4.

 

 

 

*** Optional additional question:  If you continue on getting

totals for n = 5, 6, 7, 8, ..., you will get a sequence that might

suggest a pattern to you.

 

As with all sequences, there are an infinite number of pos-

sibilities for a formula.  However, there is a formula that I have

in mind.  Whatever formula you get, do not attempt to

prove it.  Just type the formula in your reply.

 


Three 8's to make 24 (my modified version)

25 November 2014 - 05:40 AM

In each expression:

 

Use exactly three 8's.

 

Use at most three square root symbols.

 

Use at most two factorial signs.

 

You can use some combination of addition, subtraction/negation, multiplication,

and/or division signs (+, -, *, /).

 

You can use parentheses.  One pair should be sufficient.

 

Concatenation is not allowed.

 

No other numbers, operations, or characters are allowed.

 

To start off, I am giving you this expression for a solution:

 

8 + 8 + 8

 

 

> > > Try to come up with as many as five other expressions for solutions. < < <


Six sixes to make 1,000 (modified version)

25 October 2014 - 06:26 PM

Form as many horizontal-style arithmetical expressions as possible that equal 1,000.

 

In order to limit the total number of possible solutions, the following rules of mine are in place:

----------------------------------------------------------------------------------------------------------------------------

 

Use exactly six sixes.

 

Use no more than one pair of parentheses.

 

Use no more than one "/" symbol.

 

Use no more than two decimal points.

 

Use no more than one minus (subtraction) sign.

 

Concatenation is allowed.

 

No other symbols/characters/operations are allowed.