Here’s a set of puzzles that will promote the use of “backwards thinking.” That is, the technique is to look at where you want to “end” and then work backwards step by step in order to get to the beginning. Some people refer to this as “guess and check,” but that is incorrect: that technique involves putting in possible solutions and then starting from the beginning to see if the solution is correct. Eh, no, that’s not quite the way it works.In working backwards, you get to the beginning by working in reverse, undoing each of the previous actions.
These puzzles show you actually how “working backwards” really works: now, most kids would try the “guess and check” approach, which is to start at some arbitrary square and see if it goes through all the buttons. The problem is that if there are 8 squares, you have a 1 in 8 chance of getting to the correct “starter” button. If you go through 4 squares, then the changes that you’ll get it on the second shot, well, that’s a 1 in 4 chance the second time. It’s still “guess and check,” which is a valuable strategy, but not appropriate to this problem.
So there you have it: 5 different puzzles, PLUS! a “Do It Yourself” activity in which your students cut out stamps and place them on the blank matrix to make their own “working backwards” puzzles. If they make some good ones, let me know and I’ll publish them in a future update and send it to you for free!