An Important Note

Please note that the page refers to the number of slider puzzles I wrote. At the time the page was written I had only 2 such puzzles. Since then there appeared a few more. To remain meaningful the page has to be edited to reflect the changing number of available slider puzzles. Which would be bothersome as the number of puzzles grow. Please make an allowance and assume while reading the page that there are exactly two slider puzzles. In passing, there are other things impossible.

Can any one out there help me, please?

You may know that I have created two slider puzzles:

You must also know I am proud of my accomplishment. Every one can have counters at his site. Who would be crazy enough to waste one's time on just sliding counters. One must have a goal - and my puzzles, although not simple, are solvable. That is, with persistence and luck the puzzles can be solved in a finite number of steps. This is important. This is why every one likes playing these puzzles - there is the light at the end of the tunnel.

Now, it occurred to me that it would be nice to have a 'Slider puzzle' page from where all slider puzzles available at this site will be easily accessible. Like they are a few lines above. Also, I thought, it would be quite appropriate to let guests access those puzzles through a slider interface - those are slider puzzles, after all. Having written the two slider puzzles, who would doubt I can do this too. Thus I began planning a slider interface.

I have two slider puzzles. So there must be two squares #1 and #2 to provide links to the two puzzles. There also must be a square for the initial position of an 'empty square' counter. When the latter slides into #1 or #2 the corresponding puzzle would pop up. So far so good. What could be easier?

Yah, it's not difficult to write a slider interface in Java. But for just two puzzles? Is it worth it? Should I create a third slider puzzle of a different sort? But wait a moment. Assume I threw my doubts aside and returned to the original idea. Would not be such a slider access page a slider puzzle in its own right?

Indeed, what's a slider puzzle? It's a puzzle where you slide counters to achieve a certain goal. Now imagine you are looking at the Slider Puzzle page and your goal is to solve a slider puzzle. On your first move you slide a counter and then continue solving a puzzle. From the moment you conceived the notion of solving a slider puzzle and until you have solved one you would do nothing but sliding counters. Which appears to imply that from the very beginning you did nothing but solving a slider puzzle. Hooray, I thus have a third slider puzzle without much effort: just three squares with one single counter; on the first move you slide the counter into one of the available positions and proceed solving the corresponding puzzle. Was it easy. The third puzzle is solvable, too. For, the first move aside, what you get afterwards is a solvable puzzle, right? Perfect. Super. Cool. Let's do it.

But wait. Why there should be just two empty squares. Did not I just argue there is a third solvable slider puzzle? What a relief I remembered this. Would be embarrassing to provide access to only two puzzles. So let there be three empty squares. From the square #1 one gets to the first puzzle, from the #2 to the second, and from the number #3 to the third, i.e. back to the same Slider Puzzle page. Oh my, this would make the third puzzle unsolvable for one would be able to return and return and return to the same starting point indefinitely.

So it's just stupid. Be satisfied with what you have and just get going. Have two empty squares. But wouldn't this create a third solvable puzzle? And so on ad infinitum.

Do I want something impossible? There is one consolation though. Raymond Smullian cites the following:

One is morally obligated not to do anything impossible.

What a relief. No one is going to hold this against me.

Here is an excerpt from Smullyan's 5000 B.C. and ...:

A Moral Paradox.

The philosopher Jaako Hintikka makes the delightful argument that one is morally obligated not to do anything impossible. The argument, which ultimately rests on the fact that a false proposition implies any proposition, is this: Suppose Act A is such that it's impossible to perform without destroying the human race. Then surely one is morally obligated not to perform this act. Well, if Act A is an impossible act, then it is indeed impossible to perform it without destroying the human race (since it's impossible to perform it at all!), and therefore one is morally obligated not to perform the act.

References

  1. R. Smullyan, Satan, Cantor, and Infinity and other mind boggling puzzles, Alfred A. Knopf, NY, 1992
  2. R. Smullyan, 5000 B.C. and Other Philosophical Fantasies, St. Martin's Press, 1983

Self-reference and apparent self-reference

  1. Does It Blink?
  2. Apparent paradox
  3. Set of all subsets
  4. An Impossible Page
  5. Russell's paradox
  6. An Impossible Machine
  7. A theorem with an obvious proof
  8. The Diagonal Argument
  9. A link to a very similar puzzle

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