Sliding Number Puzzle

I'm not sure whether this thread belongs here or in the Water Cooler forum.

I recently saw a plastic sliding puzzle. It looked interesting so I recreated it in Excel.

The puzzle is a set of 20 numbered discs that can slide within a track. The track resembles a rectangle with semicircle ends (like an elongated oval except that the top & bottom sides are straight. I didn't top geometry!). There is a turntable that can reverse the order of 4 discs. The goal is to place the 20 numbers in sequential order.


Some thoughts/questions:

1. (SOLVED) I set up the puzzle by doing a random shuffle of numbers on Form Initialize. I'm worried that because this shuffle is truly random, it *may* create an unwinnable situation? Can anyone confirm if the puzzle can be beaten in its current version? Or how should I best go about doing a series of random valid moves to shuffle the numbers 1 to 20?
2. The labels that represent the discs should be circles. How do I change these labels to circle shapes?
3. As above but for the Frame / turntable
4. As you can see, my 'track' is very sloppy. How can I get a perfect stadium/racetrack layout (oblong with semi-circle curve on the discs on the ends)?
5. (CLOSED) Any suggestions for improving it?
6. (SOLVED) Does anyone know what this puzzle is called and/or who designed it so I can credit them in the Read Me?

Originally Posted by Pete_UK

Years (and years) ago (in the 1980's) I wrote a program to generate sliding block puzzles on a 3 x 3, 4 x 4 or 5 x 5 grid (user-selectable - I used letters of the alphabet, so couldn't allow it to be bigger), and I just generated a number of random moves to begin with. This did create unwinnable situations. I got round it by generating random numbers in the range 1 to 4 where each number represented a direction (up/down, left/right) and effectively moved a tile into the "blank" from those directions.

I had a vague idea that truly random shuffles (as opposed to doing a number of random but valid moves) could create unwinnable situations in sliding block puzzles. Thanks for confirming it.

BTW slightly off-topic but have you made any sliding block puzzles in Excel? I'd be interested in seeing it if that's OK with you.

Originally Posted by Pete_UK

As for who designed it (your number 6), I remember playing with a plastic version when I was a kid in the 60's, so I think the game has a very long history.

That's interesting. Someone has recently pointed out to me one made by Binary Arts and it's called Top Spin (TopSpin? Top-Spin?). I googled Top Spin and the pictures are the same as the one I saw. Is the same as the one you saw?

About the positioning, I've added a PlaceLabels routine to make them be circular. (I note that my routine swaps left and right.) It is based on the formula for a circle x=R*Cos(theta) y=R*Sin(theta)

I find the "how many spaces left or right" dialog box to be a distraction. A Move One Left button and Move One Right button would be smoother user interface (IMO).

About solvability. You could
1) set to correct order
2) randomly move L, move R, or Spin 1000 times
3) display the result

That way the puzzle is solvable.

I also wonder if a Label might be better than a Frame for the Turntable. A label can be placed behind the number boxes and is a little easier to control than a Frame. Since you aren't moving Boxes, but moving numbers within boxes, you know which boxes are on the turntable.

Attached is my PlaceLabel code for circularization. It is far from optimized. Run the code and press the Circlular Lable button.

Originally Posted by mikerickson

About the positioning, I've added a PlaceLabels routine to make them be circular. (I note that my routine swaps left and right.) It is based on the formula for a circle x=R*Cos(theta) y=R*Sin(theta)

I'm impressed! +1

I don't want to sound ungrateful but I only want the labels on the left and right edge to be placed in a semicircle layout (see Question 4). The track should resemble a rectangle but with the two short sides as semicircles (I'm sure there is a name for this kind of shape but if there is, I can't remember it now!)

Originally Posted by mikerickson

I find the "how many spaces left or right" dialog box to be a distraction. A Move One Left button and Move One Right button would be smoother user interface (IMO).

Good point. Thank you.

I have added these buttons to the next version. (And kept the old buttons so users can have a choice of slide input)

Originally Posted by mikerickson

About solvability. You could
1) set to correct order
2) randomly move L, move R, or Spin 1000 times
3) display the result

That way the puzzle is solvable.

I have added this to the next version.

Originally Posted by mikerickson

I also wonder if a Label might be better than a Frame for the Turntable. A label can be placed behind the number boxes and is a little easier to control than a Frame. Since you aren't moving Boxes, but moving numbers within boxes, you know which boxes are on the turntable.

Good point. I will make this change soon. (Then we can press the Turntable label to run the SPIN move)

Originally Posted by mc84excel

I only want the labels on the left and right edge to be placed in a semicircle layout (see Question 4). The track should resemble a rectangle but with the two short sides as semicircles (I'm sure there is a name for this kind of shape but if there is, I can't remember it now!)

A few google searches later.

I have come across the following names for this shape:

• Truncated Circle
• Stadium
• Obround
• Race Track

One of the answers at this page here ( http://math.stackexchange.com/questi...horse-racetrac ) has a mathematical formula which I presume will recreate the shape.

Now if I had VBA code to run this formula to set the positions of the controls on the form

While I haven't dug into your code, your earlier comment about looping through the labels got me thinking that its not necessary.

It can be arranged that the labels are fixed with lbl0, lbl1, lbl2 and lbl3 in the turntable.
An array NumberOrder(0 to 19) initially holds the values 1,2,3,...,20
A value Pointer indicates which member of the array is in lbl0, so that

lbl0.Caption = NumberOrder(Pointer)
lbl1.Caption = NumberOrder((Pointer + 1) Mod 20)
lbl2.Caption = NumberOrder((Pointer + 2) Mod 20)
Me.Controls("lbl" & i).Caption = NumberOrder((Pointer + i) Mod 20)

One rotates the track by changing Pointer.
On turns the turntable by swapping NumberOrder(Pointer) with NumberOrder(Pointer + 3) and NumberOrder(Pointer+1) with NumberOrder(Pointer+2).
Randomizing is done by rotating a random number of squares and then turning the turntable, 1000 times.

Sub RandomNumberOrder()
    Dim i As Long
    For i = 1 To 1000
        Pointer = WorksheetFunction.RandBetween(0, 19)
        TurnTheTable
    Next i
End Sub

And then I got into it and produced the attached workbook.
The size of the rotation is entered into the text box, if a number <1 or >19 is entered, it changes to the DefaultRotationValue that is set by the calling code.

With UserForm1
    .DefaultRotationValue = 4
    .Show
End With

In the attached, the labels are created and positioned by the MakeTrackLabels routine.
PostionControls is called in the Activate event because the .InsideHeight property is unreliable in the Intialize event.
This will alert the user when they have completed the puzzle. Note that 20,19,18,...,3,2,1 counts as victory as well as 1,2,3...18,19,10 and that the 1 doesn't need to be in any particular position. Also note that these conditions mean that victory will never be achieved after a Rotation, only after a TurnTheTable.

Originally Posted by mikerickson

In the attached, the labels are created and positioned by the MakeTrackLabels routine.

Incredible work. I wish I had seen this before the time I spent yesterday and today upgrading to v0.3! (v0.3 includes the suggestions from your previous post btw - I will upload v0.3 in my next post)

Originally Posted by mikerickson

This will alert the user when they have completed the puzzle. Note that 20,19,18,...,3,2,1 counts as victory as well as 1,2,3...18,19,10 and that the 1 doesn't need to be in any particular position.

Nice! I had briefly considered a win message when I first started but I dismissed it as being too hard because of how to detect a win clockwise/counterclockwise and also if 1 wasn't in position 0.

v0.3 uploaded.

I'm not certain about previous versions but this one IS winnable (even though I still haven't solved it).

Contains a number of changes suggested by mikerickson so if you like the improvements consider repping him.


LEFT TO DO:

• Add Win detection to v0.4 (This feature already created by mikerikson - see his Track.xlsm on an earlier post)
• Points 2 & 3 of OP - replace 'disk' & 'turntable' labels with circular shapes
• Point 4 of OP - alter positions of 'disks' so that the 'track' forms a perfect 'stadium' shape

Re points 2 & 3 - I've been looking into code by Andy Pope MVP. Mr Pope designed a method whereby circles can be pasted onto the userform. (See http://www.andypope.info/vba/userformdraw.htm )
My only problem is that I cant find a way to save the shapes after they're pasted - not even with VBIDE.

About the size and shape of stuff.
Nothing about this, except for the "rotate how many squares" textbox in my effort, is particularly "userform".

You could do this on a worksheet, with shapes as the turntable and as the 20 labels and make them any size you want.

I have recently lost interest in this project (the puzzle isn't much fun after working out how to solve it)(plus I have other projects on the go that are demanding focus)

So I am marking this thread as solved.


(Should anyone wish to take over and/or create their own branch/updated version - I have no objections)