1,1

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 contradiction proof eliminates the values of 18 and 22 for S.

U. Nagamani, "The magic triangles of Yates" in 'Science Reporter' pp. 65-6 Jan 1978 Vol. 15 No. 1 CSIR New Delhi.

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

Sequence in context: A041609 A041610 A042399 this_sequence A030127 A115849 A054484

Adjacent sequences: A130805 A130806 A130807 this_sequence A130809 A130810 A130811

fini,full,nonn

Lekraj Beedassy (blekraj(AT)yahoo.com), Aug 20 2007