Why is the pattern of given numbers in samurai sodukos always symmetric?
100856
I don't think it has to be symmetric.
662883
Geometrically, each letter has at least one axis of symmetry.
1175856
Some of you people are too mathematically literal than others.  Dont you combinitorial fanatics know what a combination lock is,or do you just sit in your room and do math problems?  Locks dont care about mathematical combinitorics!  They are obviously permutations.\nYea right, 3-20-14 will work on a combination lock that wants 20-3-14!!   NOT!!\n\nSo what that whoever coined the nomenclature "Combination Lock" was mathematically inaccurate?  It is really a permutation lock, and YOU KNOW IT! Or maybe you are so cloistered from human reality that you dont really know.  Get a life.
675348
I agree with chapin4ever's answer.\nand the three digit number is the ASCII equivalent of the symbol.
463413
1, 11, 21, 1211, 111221, 312211, 13112221, ....\n\nthe odd terms (reading from left to right) enumerate the number of times the same figure (which will be specified to its right) appears in the last term of the sequence.\nSo there can be at most three consecutive equal figures in a term: this happens when a figure appears a number of times equal to itself in the previous term, and also the consecutive figure (different from it) appears the same number of times. As the next figure must be different, it cannot give the same figure as a fourth after the first three.\nFor the same reason, the figure before a sequence of three equal must denote a figure different from the one which has been repeated three times, otherwise the count of that figure would have been different.
472880
If you look at the symbol to the right of the number 9 on the chart, and then the one next to the 18, and 27, infact, the symbols next to all multiples of 9 are the same.\n\nIf you subtract the quantity of each digit from any two digit number, you will always end up with a multiple of 9. So, there you go. It's known ahead of time that your nunmber will be a multipe of 9 so all multiples of 9 have the same symbol and that's the one that appears in the magic box.
779526
How are you even sure that such a function exists? the numbers look very random.
223610
Basically, why isn't there a rotational symmetry for 5 cells in a circle? Because there is no way you can have a single elementary cell that repeats itself covering all of the plane.\n\nTry filling a sheet of paper completely with identical cells of even-sided triangles, squares (and diamond shapes) or hexagons: no problem. Trying to do so with any other regular polygon will leave gaps. Hence only rotations with 2, 3, 4 or 6 periods will result in a lattice.
957153
They are simply based around counting on your fingers; fives and tens and are designed to be carved on monuments and so are mostly built of straight lines.\nThe problem with them is when you have something on the left of a number that you need to deduct, as with nine, for example.\nThat can be written as 5+1+1+1+1 (VIIII) or more economically as 10 minus one. Except the one comes BEFORE the ten: IX . That rule applies throughout, so IV is 4, XIV is 14, XIX is 19, XXXIV is 34 etc. \n\nOne tip a teacher gave me was to think of ten (X) as five (V) on top of another upside-down five. Works better if demonstrated with your hands!\nTo count to a hundred you will need the standard 1, 5 and 10 symbols; I, V and X, as well as L which is fifty (50) and C which is 100. So, IL is 49 and IC is 99.\n\nIt's really quite logical and you don't need to memorize much.
496604
Try doing this with an asymmetric figure. The translation and reflection won't give the same result.\n\nHowever, you can get any translation by doing *two* reflections one after the other.
1144759
I don't know the answer to your question, but here is a good website that might help:\n\nhttp://www.purplemath.com/modules/asymtote3.htm
1090404
look at what is added (in parentheses)\n\n2 (+1) 3 (+2) 5 (+0) 5 (+3) 8 (-1) 7 (+4) 11\n\nStarting with the first and taking every other number you have +1 +0 -1.  The other values are +2 +3 +4.  So you have two patterns interwoven.  Following those patterns will yield:\n\n2, 3, 5, 5, 8, 7, 11, 9, 14, 11, 17, 13, 20
951662
well the number to the utmost left gets added by 11 and in every row 1 gets added more than the previous row so if u see the difference between any two consecutive row is always 12 !!\nthts wat i thnk
471467
Yes. A square has an order of rotational symmetry of 4. \nThis means that if you were to rotate a square 360 degrees (1 complete revolution) about the intersection of its diagonals, you will get 4 as the number of times it takes on the initial form in terms of position and alignment.
314218
Not quite correct, consider the example of two sets of numbers:\n{1,2,3}, {2,1,3}.\nAccording to your conclusion, these sets are variants with different order of invariants. But are we always  interested in the order of invariants? If yes, order becomes no more an invariant itself. So you should reformulate your statement a bit:\n\nVARIANT IS DEFINED BY THE TYPES OF INVARIANTS IT IS BEING COMPOSED OF, AND THEIR MUTUAL ORDER IF THEIR ORDER IS NOT AN INVARIANT ITSELF. (i.e, when order matters it becomes a variant too, as in your drawings).\n\nHave further questions? Mail me: ingameswetrust@yahoo.com\nAlex.
106376
Also, if you agree that the formula for the number of combinations of n objects taken r at a time is\n\nn!/(r!(n-r)!)\n\nand that there is only one way to get a combination of n objects taking all n at a time, you'd get\n\nn!/(n!(n-n)!)  or n!/(n!0!), or canceling, 1/0! which must equal 1.\n\nSo 0! must equal 1.  More of a demonstration than a proof but it's easy to understand.
194052
I think the contributions thus far have hit upon the reason, but I'm not sure it is all tied together.\n\nChoosing any two-digit number and subtracting its separate digits will yield 81 for any two-digit number that starts with 9, 72 for a choice of 8x (8x = 89, 88, 87, 86, to 80), 63 for a choice of 7x, and so on.\n\n9*9 = 81\n8*9 = 72\n7*9 = 63\n6*9 = 54\netc\n\nIf you look at the corresponding numbers for ALL of these choices you will see the same symbol! So no matter where you start you will always get this answer.\n\nAlso, the symbols change every few refreshes of the page. So when you "Try Again?" you will get a fresh symbol. If you look at them closely you will see this happen as you go back and play again and again.\n\nThis is a very slick game, and even tho I know how it works, I still think it's way kewl.\n\nlol