It is possible to use shortcuts that reduce computational requirements or rules of thumb that avoids brute-force computational techniques. The problem of finding all solutions to the 8-queens problem can be quite computationally expensive, as there are 4,426,165,368 possible arrangements of eight queens on an 8×8 board, but only 92 solutions. Constructing and counting solutions when n = 8 He published a highly detailed description of a depth-first backtracking algorithm. In 1972, Edsger Dijkstra used this problem to illustrate the power of what he called structured programming. Gunther proposed a method using determinants to find solutions. Since then, many mathematicians, including Carl Friedrich Gauss, have worked on both the eight queens puzzle and its generalized n-queens version.
Nauck also extended the puzzle to the n queens problem, with n queens on a chessboard of n× n squares. Franz Nauck published the first solutions in 1850.
2 Constructing and counting solutions when n = 8Ĭhess composer Max Bezzel published the eight queens puzzle in 1848. If you are preparing a long file type document, sequencing the word file is recommended. Thus, this was the right way of page sequencing your MS office word file. For removing the different page numbers, you can simply select the last option from the drop down list that is “Remove page numbers”. With these options you can control the pages from where the page numbering should begin and whether you want to continue the sequence from one section to another or not. The last option provided in this dialog box is. You can also select chapter headings for separating page numbers of chapters and headings. Besides this option you have a drop down list from where you can select the patterns like. The first option is the “Number format”. This is the dialog box that opens for your advance settings for format page numbers. Go to the page number section and click”format page numbers” from the drop down list. MS office word allows you to do all of this and more and we shall illustrate the right ways of doing it. Sometimes, it may happen that you want your page numbers to start from the second page or you want to alter the numbering pattern like roman numerals instead of regular 1 2 3. Even with page number sequencing, you have a lot of options to work. MS office word provides you a lot of flexibility with almost all options. If you find it to be fine, your work is done or else you can repeat the process and modify the layout as well. You can then see the layout of the page number. Click “Close header and Footer” and the page number are ready for you. The close header and footer view button is displayed for you. In the “design” tab in the topmost row, you will have the option “Close header and Footer view” in the extreme right corner. You will find that the “Header and Footer” tab has opened.Īs you can see in the screenshot, the footer view has opened. 
After you have selected the right layout, click on the option, you would then see the page number at the designated position.You can easily see the different options available in the drop down list and select the right format that you want. Choose the alignment you want to choose be it.You can find a lot of options in the drop down list.
Scroll over to the page number section.Move over to the insert tab present in the top most rows.So, if you are not yet aware of sequencing your MS office word file, we shall provide you the right steps that can help you align the pages. Having a page number ensures that you can easily arrange the pages in the right sequence. They are extremely helpful when you need to get print outs of the word file. A lot of times you are required to insert page number in different pages of an MS office word file.
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