Magic Squares And Cubes

Cover Magic Squares And Cubes
Magic Squares And Cubes
Carus, Paul, 1852-1919
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^ ^ ?
5 5 ^ § 5^ Vi N ^ X N •0 ^ «>i ^ ?
^ J^ 5 ^ 0 N OJ -^ ^ •0 j^ R.
Sl ^ > 5 Q N § T ?
* •2 ;?
\ W Oi •0 ^ ^ > ^ -* § fl ^ N.
"5^ 5 J5 ^ •> •0 8.
{5^ ^ n ^ ^ ^ N § *5 5 ^2 5^ ^ ^ 0) 55 tJ > ^ s.
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O W J?
^ -> "o § *i J^ ^ 1 ^ J^ ^ ^ N N «0 X ^ J^ ;i ^ ^ ^ •0 A MATHEMATICAL STUDY OF MAGIC SQUARES. I35 any values to x, y, v, t and s, will yield a perfect, compound 9X9 square.
Values may lassi be assigned to x, y, v, t and ^ which will pro- duce the series i to 81 inclu
...sive. As stated before in connection with the 3 X 3 square, x must naturally equal i, and in order to produce 2, one of the remaining symbols must equal i. In order to avoid duplicates, the next larger number must at least equal 3, ^^04^1^^ and by the same ^rafeggg the next must not be less than 9 and the '^ remaining one not less than 27. Because 1 + 1 + 3 + 9 + 27:= 41, which is the middle number of the series i — 81, therefore just these values must be assigned to the five symbols uc e d in th e con - jli'ueliun u£ LliL uqiuie.

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