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A130808 Magic side-sum constants of magic triangles of Yates using the numbers 1 to 9. 0
17, 19, 20, 21, 23 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

A magic triangle of Yates, with nine numbers a,b,c,d,e,f,g,h,i has the form

           a

          d f

         e   g

        b h i c

The corner sum C = a+b+c and magic side-sum S = a+d+e+b = b+h+i+c = a+f+g+c are related by C=3*(S - 15). Since here, 1+2+3 <= C <= 7+8+9, we have 17 <= S <= 23. Finally, an argument based on a contradiction proof eliminates the values of 18 and 22 for S.

REFERENCES

U. Nagamani, "The magic triangles of Yates" in 'Science Reporter', pp. 65-66, Jan. 1978, Vol. 15, No. 1, CSIR, New Delhi.

LINKS

Table of n, a(n) for n=1..5.

EXAMPLE

All the magic triangles are illustrated:

    1         1         4         3         7

   9 6       8 9       8 1       8 7       3 6

  5   7     6   2     3   9     4   2     5   1

2 8 4 3   4 5 3 7   5 7 2 6   6 5 1 9   8 2 4 9

CROSSREFS

Sequence in context: A041610 A042399 A156656 * A194389 A030127 A115849

Adjacent sequences:  A130805 A130806 A130807 * A130809 A130810 A130811

KEYWORD

fini,full,nonn

AUTHOR

Lekraj Beedassy, Aug 20 2007

STATUS

approved

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Last modified August 14 12:27 EDT 2020. Contains 336480 sequences. (Running on oeis4.)