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%I #6 Dec 24 2015 02:40:47
%S 17,19,20,21,23
%N Magic side-sum constants of magic triangles of Yates using the numbers 1 to 9.
%C A magic triangle of Yates, with nine numbers a,b,c,d,e,f,g,h,i has the form
%C a
%C d f
%C e g
%C b h i c
%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.
%D U. Nagamani, "The magic triangles of Yates" in 'Science Reporter', pp. 65-66, Jan. 1978, Vol. 15, No. 1, CSIR, New Delhi.
%e All the magic triangles are illustrated:
%e 1 1 4 3 7
%e 9 6 8 9 8 1 8 7 3 6
%e 5 7 6 2 3 9 4 2 5 1
%e 2 8 4 3 4 5 3 7 5 7 2 6 6 5 1 9 8 2 4 9
%K fini,full,nonn
%O 1,1
%A _Lekraj Beedassy_, Aug 20 2007
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