Arranging NumbersDate: 06/26/2002 at 18:22:09 From: Rhonda Johnson Subject: Math using tile numbers Arrange the numbers 1, 2, 3, 4, 5, 6, 7, and 8 in this format: ? ? ? ? ? ? ? ? Consecutive numbers can't be adjacent vertically, horizontally, or diagonally. Use only the numbers given. For example, the arrangement 1 5 4 7 3 6 2 8 cannot be a solution because the 5 and 6 are adjacent diagonally, as are the numbers 2 and 3. I have tried for hours to solve this. Please help! Date: 06/26/2002 at 20:06:22 From: Doctor Greenie Subject: Re: Math using tile numbers Hi, Rhonda -- This is a great puzzle in logic....! I would like to just suggest something for you to think about to get started on this puzzle - to see if you can follow that suggestion through to the solution. This puzzle is so much more satisfying when you solve at least part of it on your own, rather than having somebody show you the solution. Let's start by labeling the positions as follows: A B C D E F G H The keys to the solution are positions D and E. Position D is adjacent either vertically, horizontally, or diagonally, to all other positions except position F; position E is adjacent either vertically, horizontally, or diagonally, to all other positions except position C. Now think carefully about how many numbers are adjacent to each of the numbers you have to work with. For example, there are two numbers adjacent to 3 (i.e., 2 and 4); there are also two numbers adjacent to 7 (i.e., 6 and 8). But there is only one number adjacent to 1 (i.e., 2); and there is only one number adjacent to 8 (i.e., 7). Putting the ideas of the preceding two paragraphs together tells you which numbers must go in positions D and E; once you have those numbers in place, the numbers in positions C and F are uniquely determined by the requirements of the problem; and then the rest of the solution is fairly easy. Good luck with this! Write back if you have any further questions on this... but please make an effort to finish the problem yourself before you write back. (Or, it would be great to hear back from you if my help enabled you to find the solution...!) - Doctor Greenie, The Math Forum http://mathforum.org/dr.math/ |
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