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Ding Yidong magic circles – numbers on each circle (solid colour) sum to 200 and numbers on each diameter (dashed grey) sum to 325 Ding Yidong was a mathematician contemporary with Yang Hui. In his magic circle with 6 rings, the unit numbers of the 5 outer rings, combined with the unit number of the center ring, form the following magic square :
0, 1, 3, 6, 2, 7, 13, 20, 12, 21, 11, 22, 10, 23, 9, 24, 8, 25, 43, 62, ... "subtract if possible, otherwise add" : a (0) = 0; for n > 0, a ( n ) = a ( n − 1) − n if that number is positive and not already in the sequence, otherwise a ( n ) = a ( n − 1) + n , whether or not that number is already in the sequence.
If these potential digit-sums are used in the formula 2 x digit-sum x 11, the digit-sum of the result will determine whether or not the result is an Osiris number. 1. 2 x 6 x 11 = 132. 2. Digit-sum (132) = 1 + 2 + 3 = 6. 3. Therefore 132 is an Osiris number. 1. 2 x 7 x 11 = 154. 2. Digit-sum (154) = 1 + 5 + 4 = 10. 3. Therefore 154 is not an ...
In mathematics, summation is the addition of a sequence of numbers, called addends or summands; the result is their sum or total.Beside numbers, other types of values can be summed as well: functions, vectors, matrices, polynomials and, in general, elements of any type of mathematical objects on which an operation denoted "+" is defined.
The first few values are 0, 1, 2, 4, 6, 10, 12, 18, 22, 28, 32 (sequence A002088 in the OEIS). Values for powers of 10 at (sequence A064018 in the OEIS ). Properties
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This sum can also be found in the four outer numbers clockwise from the corners (3+8+14+9) and likewise the four counter-clockwise (the locations of four queens in the two solutions of the 4 queens puzzle [50]), the two sets of four symmetrical numbers (2+8+9+15 and 3+5+12+14), the sum of the middle two entries of the two outer columns and rows ...
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