A130808 Magic side-sum constants of magic triangles of Yates using the numbers 1 to 9.

17, 19, 20, 21, 23

Offset: 1

Author

Lekraj Beedassy, Aug 20 2007

Keywords

• fini
• full
• nonn

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.

Examples

			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
		

References

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