In Wartune Patch 6.3, Magic Square will be replacing Tower of Kings. This guide will explain an efficient way to full rewards! Magick squares are an arrangement of numbers in a square grid where the numbers in each row, and in each column, and the numbers that run diagonally in both directions, all add up to the same number. A magick square also has the same number of rows as it does columns. This magic square adds up to 34. This is the smallest sum possible using the numbers 1 to 16. Keep this card and you’ll be able to perform this stunt any time you wish.
A magic square is a 3×3 grid where every row, column, and diagonal sum to the same number. How many magic squares are there using each the numbers 1 to 9 exactly once?
Prove there are no other possibilities.
I’ve posted a solution in a video.
Or scroll below for a text/image summary.
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'All will be well if you use your mind for your decisions, and mind only your decisions.' Since 2007, I have devoted my life to sharing the joy of game theory and mathematics. MindYourDecisions now has over 1,000 free articles with no ads thanks to community support! Help out and get early access to posts with a pledge on Patreon.
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Answer To: How Many 3×3 Magic Squares Are There?There are 8 ways to make a 3×3 magic square.
In fact, there is really only one pattern. Every other pattern is a rotation or reflection. From the upper left, the first square on the right is a reflection through the center (transposes columns 1 and 3), for example.
Now let’s prove these are the only possibilities.
You could program all 9! = 362,880 possible ways to place the numbers in the square and test it out. But there is a nice way to prove it logically.
The proof proceeds in 5 steps.
Step 1: The magic sum is 15
By definition, every row, column, and diagonal has the same sum M.
Thus each of first row, second row, and third row has a sum of M. So the first 3 rows sum to 3M.
On the other hand, if we sum up all 9 elements, we must have the sum of the numbers 1 to 9.
This means 45 = 3M so 15 = M.
If a magic square exists, then each row, column and diagonal has to be 15.
Step 2: Combinations that sum to 15
Suppose you use the numbers 1 and 2.
1 + 2 = 3
You would need 12 in order to make 15. This is not possible since we are using the numbers 1 to 9. So we can’t combine 1 and 2 to make 15.
Magic Square Wartune Game
Classic menu for office 2010 free. download full. Since 9 is the largest number, we have 1 + 9 = 10, which means our other number has to be 5.
1 + 5 + 9 = 15
Then the next largest number is 8, so we can have:
1 + 6 + 8 = 15
We can’t make a sum with 7, since we would need two 7’s to make that possible:
1 + 7 + 7 = 15
We can go through this exercise and find there are only 8 ways to get to 15.
Step 3: the center square is 5
The center square is involved in the middle row, the middle column, and both diagonals.
Which number is involved in 4 sums of 15? There is only one! This is the number 5.
Step 4: the corners are even; the edges are odd (1, 3, 5, 7)
Similarly, each corner square is involved in a row, a column, and a diagonal sum. The only numbers involved in 3 sums are even numbers.
By the same logic, the edge squares could be the odd numbers 1, 3, 5, and 7.
Step 5: enumerating the 8 possibilities
The number 1 can go in any of the 4 edges.
The number 9 will be forced to be opposite.
The number 3 must go in the perpendicular row to the left or right side of the 1, or in the perpendicular column to above or below the 1.
In all there are 4×2 = 8 possibilities. Since each odd number is involved in two sums, the remaining numbers are forced by these choices.
If you look at the first square, the other 7 squares are rotations or reflections. (you can see an animation of this idea in my video).
Wartune Magic Square Pattern
So there is 1 unique magic square. The eight patterns are rotations and reflections that correspond to symmetries of a square (the dihedral group of order 8).
It’s a pretty neat proof, and we didn’t have to test all 9! = 362880 possible ways to place the numbers in the square. Samlogic usb autorun creator crack windows 7.
Magic Square Wartune
##### 1) Basics which you should've learned alreadyTo start things off I'll have one picture explaining you the basics of Magic Square. Honestly I shouldn't even need to do this, but since I know PEBCAK happens quite often I'll do this one picture for the sake of wasting my time:![](https://image.ibb.co/mWLXrk/Magic_Square_Basics.png)So basically kill all the mobs on the squares which I've coloured green, then finally kill the square that I coloured blue and that's it. Do not kill anything which I've coloured orange. If you follow this pattern correctly you'll reach 24K points after lvl 6 **at worst**.If this paragraph is too short for you to learn the basics you should watch some Wartune Youtube videos or read some DolyGames blog posts or whatever.##### 2) Pattern Break: Why, How and when?The *'Pattern'* is basically the order of kills which you should know as somebody who ran Magic Square before. If you did not, then the pattern is briefly explained in paragraph 1. A *'Pattern Break'* in my definition basically describes a special case where you want to kill a forbidden mob square, which in paragraph 1's screenshot is located on one of the eight squares that I coloured orange. This special case is exclusively and only when a **green buff** is located on a forbidden mob square.**Why?)** If you have any reading comprehension and read the description of the green buff *(Points received within 1 minute +50%)* you know exactly why green buffs are useful. If you utilize it the way you should, you can skip an entire level. If you have one green buff for example, you'll reach 24K points after lvl 5. If you have two you'll be so close at 24K points after lvl 4 that literally 1 or 2 more lines of 4 will make it. Etc. Etc.**How?)** A pattern break is basically clearing a line of 4, or 5 if your party is doing it wrong.![](https://image.ibb.co/doHj45/Pattern_Break_standard.png)In this picture you'll see an example on one of the four border lines. If we pretend that the green coloured circle is our green buff, then the red circles the four mobs that need to be killed in the specific situation. As you can see my standard is basically to kill the corner mob 'closest to the green buff'. If everybody follows this standard it can prevent the death of 5 mobs. The less mobs die in a pattern break, the less stronger mobs you get at the end. *With the two examples I've drawn in picture I'll expect anybody who reads to automatically understand which four mobs to kill if a green buff appears on one of the other 6 forbidden squares. (And if that's not the case I'll be very disappointed in humanity's comprehension capabilities)***When?)** Green buffs are generally useful supportive items towards 24K points, but you certainly don't need an infinity number of them. Here are some examples:* if you're already at lvl 6 about to kill them for the final points to 24K, then using a green buff won't speed up your process of 24K points by an entire level anymore since lvl 7 is pointwise not needed anymore. * If you're at the lvl 5 with only the center mob remaining, then using the green buff before making the final kill can skip you the need of clearing lvl 6.* If you're at lvl 4 and have two green buffs, you'll consume one at lvl 4 and reach lvl 5 with a higher number of points that's still below 24K. At this point you'll notice that whether you use the second green buff or not, you still won't skip an entire level. **Therefore if you're at lvl 4 having one green buff already, you don't need to pattern break for a second green since there's no real benefit.*** If you're at lvl 3 you can take benefit of two green buffs, you'll consume one at lvl 3 and the second at lvl 4. Once you've gone past lvl 4 that way your points will be so extremely close at 24K that you no longer need to stick to the pattern at lvl 5 anymore. In such a lucky situation you can begin bonus chest hunting directly at lvl 5 and let the miracle of time grant you the last few points towards 24K.##### [Theoretical] best post-24K strategyThe general rule which everybody (should) understand is to reach (or very closely approach) 24K points as fast as possible so you'll have more time left for the bonus chests. What most people don't realize is this: **The wave that randomly spawns buffs and bonus chests by luck happens once per round minute, or in other words x:00 in which x is a random integer between the 1 and 14.** Therefore your party can approach the best chance of having one (or more) bonus chest appear on the board if **all mobs are alive standing on empty squares per x:00 minute**. For example if 16 mobs of your standard pattern has died whilst the remaining 9 squares (the 8 forbidden square and the center square that needs to be killed last) are occupied with buffs, whilst the timer just ticks at 13:00: Then for the 13:00 wave zero bonus chest can be spawned since there's no empty yet active square left for it to reside.As conclusion of that we've got the following post-24K points rules for the theoretical best chance of bonus chests disregarding serversided codes:1. Try to have as many mobs alive as possible, each time the timer ticks near x:00 seconds.2. Do not kill mobs which empty squares at random.3. Mobs that stand on squares occupied by buffs can be killed of course, since chest can't spawn on that spot anyway.4. Keep an eye on the timer and only clear lines or combo-lines involving buffs at x:59, so you have 59 seconds to finish the clear and have new and empty mobs spawn in before the timer hits (x-1):00.5. Just have common logic to determine combos if you see multiple chests or buffs on the board which may be grab'able at once. I'll have a couple of very-obvious examples drawn in picture below just in case PEBCAK:![](https://image.ibb.co/fCZ8Wk/Example_1.png)In this example you'll kill everything that's circled green, choose one of the two mobs that's circled yellow-green'ish depending on which one's weaker and finally kill the blue circled mob after everything else died.![](https://image.ibb.co/nAowHQ/Example_2.png)In the second example you have three options to get the bonus chest. Two of the three options involves killing hypothetical lvl 9999 mobs that are obviously stronger than you. The best option is obviously killing the easy lvl 1 mobs. In reality many people seem to forget that lines don't always need to be straight, as long as your brain is straight *(cough cough as long as you're not out of the closet as a person)*.