This Robotic Arm Can Do Many Things, But Is Unable To Think For Itself

This problem is very similar to the Tower of Hanoi.

Let's first start by experimenting a bit.

In order to move the first box, there must be one move - you just move the box to another spot. However, in order to move the second box, you must move it to a different spot first, since you cannot place it on top of a smaller box, and then put the first box on top. To move the third box, you put it on a separate spot from the first two, move the first box to a separate spot, move the second box onto the third box, and move the first box back onto the second box.

If we continue this process, we will find that to move the $n^{th}$ box, we need to perform $2^{n-1}$ moves, and if we want to move $n$ boxes, we will need to perform $2^{n-1}+2^{n-2}+\ldots+2^2+2^1+2^0 = 2^n - 1$ total moves.

In this problem, we must move six boxes, so the total number of necessary moves is equal to $2^6-1=\boxed{63}\ \blacksquare$

Tower Of Hanoi Problem..... solution is easy.... rules is: ways=2^n-1

1 box = 1, 2 boxes = 3, 3 boxes = 7, 4 boxes = 15

We can clearly see that each one is one bigger than twice the previous one. So we just continue this until we reach 6 boxes

5 boxes = 2(15)+1= 31, 6 boxes = 2(31)+1= 63

So 63 is the answer.

I did the solutions for the same situation but with 2, 3, and 4 boxes, and guessed that the solution (minimum number of moves to stack the boxes to the rightmost space) for $N$ boxes could be modeled as:

$2^N - 1 = M$

Where $M$ is the minimum number of moves necessary to stack the boxes to the rightmost space.

$2^6 - 1 = \boxed{63}$

I guess I just got lucky.

This is equivalent to the Tower of Hanoi problem, in which discs are moved from one column to another with an empty "intermediate" column. If you look at the description, you see that the solution for the problem with $n$ discs (or in this case, $n$ boxes) are moved from one spot to another is $2^n - 1$ moves. In the case of 6 boxes, $2^6 - 1 = \boxed{63}$ moves are required.

This is a standard tower of Hanoi problem, the answer being 2^n - 1.

dilihat dari struktur deret bilangan yang memiliki fungsi 2^n-1, 2^n-2,2^n-3......... 2^1, 2^0 maka rumus fungsi menjadi 2^n - 1 & subtitusi 6 pada n jadi jawabannya 63

This is just the Towers of Hanoi puzzle with 6 disks. The solution is 2^6 -1

It is a "Tower of Hanoi" problem in a subject called Data structures. It says, if you have to arrange the disks from a source to a destination (with one temporary spot needed), then you can do it in 2^n - 1 moves, where n=no. of disks.

Here instead of no. of disks, boxes are given. So substitute the number of boxes as n in the formula and calculate the answer. Ans. = 63

it is never allow to place any box on top of smaller box but we can use the second vacant location to keep temporarily big box= and then replace all boxes in right manner according to given condition if let three is one object number of move =2^1 - 1=1 if n=2 number of move=2^2 - 1=3 if n=3 number of move=2^3 - 1=7 ......... n=6 number of move=2^6 - 1=63

Classic Towers of Hanoi problem

Minimum number of moves required to solve for n boxes = $2^{n} - 1$

Source: http://en.wikipedia.org/wiki/Tower of Hanoi

This problem is like the Tower of Hanoi in which you need to move a stack of discs in a peg into another peg. There are three pegs used and the same conditions are given. The minimum number of moves that can be made to move this stack of discs is $2^n - 1$ where n is the number of discs. Therefore n = 6 and $2^6 - 1 = 63$