Mathematical Questions and Solutions Volume 36
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Mathematical Questions and Solutions Volume 36

Mathematical Questions and Solutions Volume 36


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This historic book may have numerous typos and missing text. Purchasers can download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1881 Excerpt: ... numbers greater than 8, and then striking out 1612 5, 1698 as containing numbers not repeated. The list then becomes 16 13 4 15 14 4 14 13 6 13 12 8 16 11 6 15 12 6 14 12 7 16 10 7 15 10 8 14 11 8 Now for the six ranees including 1 there must he two with 16, and there are three sets which may easily be filled up, thus--By taking the differences of these from 17, we get the ranges of which 16 is a member, namely--1 4 13 1 4 13 1 6 11 1 6 11 1 7 10 1 7 10 2 3 13 2 3 13 2 6 11 25 11 279 279 369 36 10 36 10 469 459 369 We are now able to form any square, and to tell the number of arrangements. First, place 1 in any of the 16 positions. Secondly, put 16 in any one of the 9 places in rauge with 1. Thirdly, choose any one of the three possible pairs of ranges with 1 and 16. Fourthly, place in range the numbi-rs so chosen. This can be done in 8 ways, as will be seen by the example to be given presently. The square can now be completed in only one way, which is determined by considering the necessary ranges of which 16 forms an element. Thus there are 16x9x3x8, or 3456 variations. But these include repetitions, such as may be made by turning the square round, bringing each side in succession to the top, and by reversing the order of the rows or columns. These two causes bring about eight variations for each distinct set. There are, therefore, 432 essentially different arrangements. Example.--Place I at j. Place 16 at /, giving the fifth symmetrical system. Chose the 16 13 4, 16 10 7 set of ranges. Then we obtain the tight partly formed squares--. 10. 7. 7. 10. 10. 7. 7. 10 13 I 4 16 13 1 4 16 4 1 13 16 4 1 13 16 To complete these, remember that 2 mast be in range with 16, 7 and 16, 13. This gives as its places in the above eight squares, h, e, q, p, p, q, e, h. The ..


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Product Details
  • ISBN-13: 9781236252166
  • Publisher: Rarebooksclub.com
  • Publisher Imprint: Rarebooksclub.com
  • Height: 246 mm
  • No of Pages: 32
  • Spine Width: 2 mm
  • Width: 189 mm
  • ISBN-10: 1236252160
  • Publisher Date: 01 May 2012
  • Binding: Paperback
  • Language: English
  • Returnable: N
  • Weight: 77 gr


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