![]() How many ways can you make a 2-by-1 walkway (silly as it sounds!)? One, of course: Sometimes it only builds our understanding of the problem, but in others (as in inductive proofs) it becomes part of the solution. This is a very important step of problem solving, which I have elsewhere called the exploratory phase. And in this case, that leads directly to a solution. That usually means simplifying the problem by working with smaller, easier numbers - actually, that's more or less what children's play is, isn't it? By trying things out in a smaller case, I get a feel for how it works. When I don't see how to solve a problem like this, I start by playing with the ideas involved in the problem. But here, we’ll be finding a pattern, just as Dawn suggested. In fact, we’ll be doing that for one of these problems later. On the surface, this is a combinatorics question, counting ways to do something and we might approach it with permutations or combinations. Here are three of the many ways to lay the bricks: I know there has to be a pattern, but I do not see it. How many different ways can I build this walkway? The bricks can lie vertically and horizontally but in no other direction. The first, from 2002, is the most basic: Laying a Brick Walkway ![]() The first set (here) are direct representations of Fibonacci, while the second set will be considerably deeper. Here and next week, we’ll look at a collection of word problems we have seen that involve the Fibonacci sequence or its relatives, sometimes on the surface, other times only deep down.
0 Comments
Leave a Reply. |
AuthorWrite something about yourself. No need to be fancy, just an overview. ArchivesCategories |