Experience Seamless Navigation with the LG Magic Remote Original

The LG magic remote original is a unique and advanced remote control that is specifically designed for LG smart TVs. It offers a wide range of features and functionalities that enhance the viewing experience and make navigation easier. One of the key features of the LG magic remote original is its point and click capability. It has a built-in cursor that allows users to simply point at the desired option or content on the TV screen and click to select it. This feature eliminates the need for manual scrolling and button pressing, making it more intuitive and user-friendly. Another notable feature of the LG magic remote original is its voice recognition technology.

Bernie Westacott, Twitter

Even if it only took one second to arrange the numbers and check whether a solution has been found, you would need to allow over one hundred hours to complete the task. If only 2 are given and for the hardest level the centre value M is never given then M can be chosen freely and the other 2 given values would determine A and B.

Another notable feature of the LG magic remote original is its voice recognition technology. With this feature, users can simply speak into the remote control and command the TV to perform various tasks. Whether it's changing the channel, adjusting the volume, or searching for a specific program or movie, users can easily do it with just their voice.

Magic squares unblocked

A 'Magic Square' is a square of 3×3 numbers where the sums of all numbers in a row, in a column and in both diagonals are all the same.

Typical question:
What number has to replace the question mark to complete the diagram as a Magic Square?

15 * 35 50 * ? 25 * *

This is easy to solve. The sum in each line is 15+50+25=90. From the diagonal, it follows that the middle value is 90−25−35=30 and from the 2 nd row: 50+30+?=90 ⇒ ? = 10.

How would you solve a Magic Square with fewer given numbers, like the one below?

? * * * * 47 * 63 *

P Q R U V 47 X 63 Z

P+Q+R = U+V+47 = X+63+Z = P+U+X = Q+V+63 = R+47+Z = P+V+Z = R+V+X,

and solve this system of equations by eliminating all unknowns except P to get one equation for P and solve that. These are 7 conditions for 7 unknowns.

• Let us look for simple relations between the numbers in the Magic Square.

Because a square has many symmetry operations (4 rotations + mirroring and their combinations), let us define quantities which do not change under such symmetry operations. For example, if our square is

P Q R U M W X Y Z

then these quantities that do not change under rotations and mirrorings are

C = sum of corner values (= P+R+X+Z) E = sum of middle edge values (= Q+U+W+Y) M = middle value (= M) S = sum in each line (= P+Q+R = P+U+X = X+M+P = . ) .

• It is not difficult to find the following relations between C, E, M, S by eliminating variables P, Q, R, U, W, X, Y, Z from the above equations.

2C + E = 4S (1) M + C + E = 3S (2) C + 2M = 2S (3) C − M = S (4) 3M = S (5)

The above relations result as follows: (1) from summing the 4 edges
(2) from summing all numbers
(3) from summing the 2 diagonals
(4) from (1) − (2)
(5) from (3) − (4) ▢ Verify (1), (2) and (3) by replacing C, E and S by their sums.

How can they help? For example, relation (5) is enough to solve the following examples.

3 2 7 * ? * * * *

Since all 3 numbers in the 1 st row are given, we know that S = 3+2+7 = 12. Thus by (5), ? = 12/3 = 4.

11 * 4 * 6 * * ? *

Let Q = the middle value of 1 st row. Then by (5), 11+Q+4 = 3×6 ⇒ Q = 18−4−11 = 3. Thus, ? = 18−6−3 = 9.

* * 5 * 9 * ? * *

* * 5 * ? * 9 * *

Example: The following puzzle contains the numbers 7. 15. What is the value of P?

P * * * * * * * 14

Without knowing that this Magic Square is filled with the whole numbers from 7 to 15 inclusive, the one given number would not have been enough. But with this information and by (5), 3S = (7+15) + (8+14) + (9+13) + (10+12) + 11 = 4×2 + 11 = 99 ⇒ S = 33 ⇒ M = 11 ⇒ 14 + 11 + P = 33 ⇒ P = 8.

How about the problem below?

? * * * * 47 * 63 *

0 0 0 0 0 0 (6) 0 0 0

and find 'deformations', i.e. methods to change the Magic Square into another Magic Square. The first such deformation is to add the same value 1 to all fields:

1 1 1 1 1 1 (7) 1 1 1

Before looking for more possible deformations, we first use a handy definition.

• The set of integers is closed under addition, i.e. adding any two integers together results in an integer.
• The set of real numbers is not closed under division (but is closed under non-zero division, i.e. division by numbers that are not 0).

a11 a12 a13 a21 a22 a23 (8) a31 a32 a33

b11 b12 b13 b21 b22 b23 (9) b31 b32 b33

a11+b11 a12+b12 a13+b13 a21+b21 a22+b22 a23+b23 (10) a31+b31 a32+b32 a33+b33

a11+b11 + a21+b21 + a31+b31 = a11+a21+a31 + b11+b21+b31 (commutativity of addition) = a12+a22+a32 + b12+b22+b32 (because (8) and (9) are Magic Squares) = a12+b12 + a22+b22 + a32+b32 (which we wanted to show)

a11 a12 a13 a21 a22 a23 a31 a32 a33

b×a11 b×a12 b×a13 b×a21 b×a22 b×a23 b×a31 b×a32 b×a33

a11 + a12 + a13 = a21 + a22 + a23 then b×(a11 + a12 + a13) = b×(a21 + a22 + a23) and b×a11 + b×a12 + b×a13 = b×a21 + b×a22 + b×a23 .

Corollary 1.1:
Applying this theorem means that subtracting the middle value from all fields of a Magic Square (i.e. subtracting M times Magic Square (7)) gives a Magic Square with middle value 0.

Let us go back to our problem of finding other deformations. The next one should keep the centre value as 0 in order to not interfere with the deformation −M×(7).
Let us change the upper-left to 1 (the smallest possible value):

1 * * * 0 * * * *

1 * * * 0 * * * −1

+1 −1 0 −1 0 +1 (11) 0 +1 −1

This is a Magic Square itself.

We get another deformation of a Magic Square through a symmetry transformation. This means that any mirroring or rotation of a Magic Square also gives a Magic Square. Mirroring on the main diagonal does not give a new Magic Square, but rotation does give a new Magic Square:

0 −1 +1 +1 0 −1 (12) −1 +1 0

We now apply theorem 1 three times.
Given a Magic Square, first we subtract the square a22×(7) to make the middle value zero. We then subtract from the new square the square a11×(11) so that the upper-left corner becomes zero. The middle stays zero because a11×(11) has middle value 0. Then a square a13×(12) is subtracted so that the upper-right corner becomes zero. In doing that, the middle value and the upper-left corner stay zero because these fields are zero in a13×(12). So, that means that one can subtract from any Magic Square suitable multiples of squares (7), (11), and (12) to obtain a Magic Square of the form

0 * 0 * 0 * * * *

with an S value of zero (because the middle value is zero). This easily shows that the whole Magic Square is

0 0 0 0 0 0 0 0 0

But, that means each Magic Square can be written as a sum of multiples of squares M×(7) + A×(11) + B×(12).

Theorem 2:
Each Magic Square can be written in the form

M+A M−A−B M +B M−A+B M M+A−B (13) M −B M+A+B M−A .

As shown above, each Magic Square can be reduced to the square consisting of only zeros by subtracting multiples of (7), (11) and (12).

In more mathematical language one would say that:
The Magic Squares (7), (11) and (12) are a complete set of generators for all Magic Squares.
Now that we know the essence of all Magic Squares, is this all that useful in solving Magic Square problems? With rule (5): 3M = S we found a simple and useful relation between a single component of the square and S. Here are two more.

Lemma 2:
Each corner value is the average of the 2 values adjacent to the diagonally opposite corner.

For example, in the upper-left corner in (13), M+A = ((M+A+B)+(M+A−B))/2, and likewise for the other 3 corners.

? * * * * 47 * 63 *

by reducing it to ? = (63+47)/2 = 55. Here is another relation:

Lemma 3:
For each line through the middle of the square, the middle value M is the average of the other two values in the line.

By inspection of (13).

Corollary 2.1:
If nothing but a single number is given, then no other number can be determined.

Corollary 2.2:
If 2 numbers are given and lemmas 2 or 3 apply, then a 3 rd number is fixed.

Corollary 2.3:
If 3 numbers are given which are not related through lemmas 2 or 3 then these 3 numbers determine the whole Magic Square.

• When we look at Magic Square (13) we see that there are 3 independent parameters A, B, and M. If only 2 are given (and for the hardest level the centre value = M is never given) then M can be chosen freely and the other 2 given values would determine A and B.

• By choosing M=0 as the centre value, all lines through the centre can be completed simply by switching the sign of the opposite number to get a sum of 0. For the remaining numbers, one only has to do two differences/sums of two numbers.

* 80 * * * 56 * * *

* 80 * * * 56 68 * *

* 80 −68 −56 0 56 68 −80 *

Finally since all sums are 0, the upper-left corner must be 68−80 = −12. Therefore, the simplest solution of this example is:

−12 80 −68 −56 0 56 68 −80 12

• If we know all numbers in one line and 2 numbers in a line that crosses it, then we can speed up computation slightly, especially when numbers are larger.

P * * U ? W X * *

• We learned a general approach for solving a difficult mathematical problem (here finding the most general Magic Square) which has symmetries (here rotations and mirror symmetries) and a special solution (here the Magic Square (11)) which does not have all these symmetries ((11) is not rotationally symmetric) such that when one applies the symmetry operation, a new special solution is generated (here (11) → rotation → (12)).
  Furthermore, we saw how in problems for linear objects the general solution can be obtained by adding multiples of a complete set of special solutions (here each Magic Square can be written as a sum of multiples of (7), (11) and (12)).

Learning and understanding Mathematics, at every level, requires learner engagement. Mathematics is not a spectator sport. Sometimes traditional teaching fails to actively involve students. One way to address the problem is through the use of interactive activities and this web site provides many of those. The Go Maths main page links to more activities designed for students in upper Secondary/High school.

The LG magic remote original also offers gesture control, allowing users to control their TV with simple hand movements. By waving or swiping their hand in specific directions, users can navigate through menus, adjust settings, and perform other actions. This feature adds a fun and interactive element to the TV-watching experience. Furthermore, the LG magic remote original comes with a universal control feature, which means it can be used to operate other devices connected to the TV, such as set-top boxes, gaming consoles, and sound systems. This eliminates the need for multiple remote controls and simplifies the overall control process. In terms of design, the LG magic remote original is sleek and ergonomic, making it comfortable to hold and use for extended periods. It also has a built-in microphone for voice commands and a scroll wheel for easy scrolling through menus and web pages. Overall, the LG magic remote original is a powerful and convenient accessory for LG smart TVs. Its advanced features, such as point and click, voice recognition, gesture control, and universal control, make it a valuable addition to any home entertainment setup..

Reviews for "The Magic in Your Hands: Exploring the Design of the LG Magic Remote Original"

1. John - 2 out of 5 stars - I purchased the LG Magic Remote Original with high expectations, hoping to streamline my TV watching experience. However, I found the remote to be quite unresponsive and difficult to navigate. The buttons are too small and close together, making it easy to press the wrong one. Additionally, the voice recognition feature is hit or miss, often misinterpreting my commands. Overall, I was disappointed with the performance of this remote and wouldn't recommend it.

2. Sarah - 3 out of 5 stars - The LG Magic Remote Original is an interesting concept, but it fell short in terms of functionality. The motion control feature is gimmicky and doesn't work consistently. It often responds too slow or not at all, making it frustrating to use. While the layout of the remote is intuitive, the build quality feels cheap and flimsy. Despite its shortcomings, the remote does have some convenient features like the scroll wheel, but overall, it didn't meet my expectations.

3. Mark - 1 out of 5 stars - I regret purchasing the LG Magic Remote Original. The remote frequently freezes and requires a restart, which is incredibly frustrating. The touchpad is also overly sensitive and difficult to control. The remote's battery life is abysmal, constantly needing to be replaced or recharged. I expected better quality and performance from LG, and this remote did not deliver. I would not recommend it to others.

Unlock the Full Potential of Your LG Smart TV with the Magic Remote Original