POPULAR SCIENCE 



87 



Hutton gives various rules, some original, some derived 

 from previous writers, for the formation of such squares, but 

 it will suffice here to reproduce the result so far as a 16-cell 

 square of the first sixteen numbers is concerned : 



Hutton's 34 Square. 



This solution fulfils the requirements of his definition, but it 

 falls short of the claims for the Dudhai square, in that some 

 only of the sub-squares total 34. 



Popular attention having been directed to the 34 square 

 by a competition in one of the weekly journals some thirty 

 years ago, the following solution was arrived at : 



It was found to possess the following, at first sight " super- 

 magic," properties, which I give in extenso for the benefit of the 

 curious, without entering into any explanation as to how the 

 possession of certain properties is involved as a natural sequence 

 to that of others. The following each total 34 : 



(a) All rows, columns, and diagonals. 



(b) All sub-squares of four numbers. 



(c) The four corner numbers. 



(d) Parallel semi-diagonals, e.g. (1 -j- 7+ 16+ io), 

 (IS + 9 + 2 + 8), etc. 



(e) Parallel quarter- and three-quarter diagonals, e.g. 

 (14 + 9 + 3 + 8), (11 + 1 + 6 + 16), (4 + 7+i3 + io)» etc. 



