



This page is about three closely related puzzles:
Spinout by Binary Arts (now called Think Fun), is a simple puzzle consisting
of a long flat plastic rectangle inside a grey cover. The piece could simply slide
out if it were not for 7 oddly shaped dials. If all the dials are turned horizontal
it will slide, but a dial can only be turned if the one to its right is vertical
and any others further to the right are horizontal. This puzzle is now sold
as Elephant Spinout, with a new design where the dials have little elephant
figures on them, and a nice release mechanism so you can reset the dials.
There is an interesting design flaw in the Spinout that allows for an
unintended shorter solution. The smaller versions of Spinout made in
Taiwan and which have dials of different colours, have an especially
short alternative solution.
Spinout was invented and patented by William Keister (US 3,637,215, filed 22 December 1970, granted 25 January 1972). This is the fourth puzzle Binary Arts made, and the first successful one. Their first puzzle was the Hexadecimal Puzzle, also by Keister.
The Brain, by MagNif, consists of a tower of eight transparent disks that can rotate about their centres. The disks have slots in them and there are eight upright black rods going through the stack. The rods have two positions, in or out, and the aim is to move all the rods out. The rods are numbered 1 to 8, and a rod can only move if the rod with the next lower number is out and the further lower rods are in.
The Chinese rings puzzle is a row of rings, each affixed to a base with a rod. Each ring encloses the rod of the next ring in the row. A long loop of wire goes through all the rings and around all the rods. A ring can only be released from or placed back on the loop if the next ring is on the loop but all other rings further down are already off.
If your browser supports it, you can click on the link below to see a Javascript version of the Spinout puzzle.
All three puzzles have the same basic solution, which is based on the (standard) binary Gray code. In essence a binary Gray code is a list of all binary numbers of a certain length in such an order that any two adjacent numbers in the list differ only by one digit. This obviously corresponds to the puzzles, where each dial/rod/ring has two positions and you can only move one at a time.
All these puzzles are quite simple. In any position there are at most two possible moves, the equivalent of going up or down the list of Gray code numbers. If you never take back a move, you will always go on until you reach the end/beginning of the list. Unfortunately the actual puzzle might only be solved at the other end of the list, and you will have to go all the way back.
With the Chinese Rings and Spinout you have two choices for your first move, either ring/dial 1 or 2. If there are an even number of rings/dials, then you must begin with the even ring/dial i.e. number 2, if there are an odd number of rings/dials (the standard spinout has 7) then begin with the odd one i.e. number 1.
If you begin with the wrong move, you end with the position where all but the last ring/dial is off the loop/horizontal. You must then go all the way back to the beginning, and then do twice as many moves again to solve the puzzle. Note that with Spinout, there is a shortcut solution you can use in this situation (see below).
With the Brain you only have one first move, so it is easy to solve. Once in the solved position there are two choices for the next move if you want to bring it back to the initial position. Since there are an even number of rods, your next move then must be rod 2.
Suppose you find one of these puzzle in an intermediate position, and want to determine which of the two moves you need to solve it from there. The way to deduce this is best shown by a few examples.
Suppose the rods 18 of the Brain are In/Out/Out/In/Out/Out/In/In. If you want to solve it, then you would want the most difficult rod to move, rod 8, to be moved out. To do this, you must have rod 7 in and 16 out. Rods 57 are already in that position, but 4 is not so that has to be moved first. To move rod 4 you must have rod 3 in and 12 out, so rod 3 must be moved first. Therefore we need rod 2 in and rod 1 out. To move rod 2 in, we must have rod 1 in. This is already the case, so we can move rod 2 to get closer to the solution.
A similar argument would work if we wanted to get back to the starting position, all rods in. In that case we must move rod 6 in; to do that we need rod 5 in first; for that we need 4 in and 13 out; hence we must move rod 1.
On spinout we could make the same kind of argument. The dials are numbered 17 where dial 1 is the one that can always be moved, . Being righthanded I have dial 1 on the right, so in the starting position all the dials point upwards. Suppose they are all horizontal except 2,5,7. To move 7 horizontal we need 6 to be vertical. To move 6 we need 5 vertical and 14 horizontal. Therefore we need to move 2 horizontal and to do that 1 must be moved vertical first.
This argument also shows why we must turn dial 1 first in the starting position where all 7 dials are vertical. Dial 7 must be moved horizontal, so we need 6 vertical and 51 horizontal. To get 5 horizontal we first must get 4 vertical and 31 horizontal. In order to get 3 horizontal we must have 2 vertical and 1 horizontal. Therefore dial 1 must be moved first.
Solution Length:
The length of the solution (for any sized puzzle) can be easily calculated by
recursion. Let L_{n} be the solution length for a puzzle with n
dials/pins/rings. Clearly L_{1}=1 and L_{2}=2. To solve a
puzzle with n pieces, first we have to solve the first n2 pieces, move the
nth piece, unsolve the first n2 pieces, and finally solve n1 pieces. So
we find that L_{n} = L_{n1} + 2·L_{n2} + 1.
This eventually leads to a simple formula, L_{n} = [2^{n+1}/3],
where the square brackets denote rounding down to an integer. This gives
L_{7}=85, so the standard Spinout needs 85 moves. The Brain needs
L_{8}=170 moves.
As mentioned above, there is an design flaw in the Spinout that allows for an unintended shorter solution. This is possible because the frame is too short, so that when the slide is extended beyond the frame, the dials on the outside can twist without restriction. Thanks to Tim Rowett who passed this on to me.
The shortcut solution is as follows:
a.  Turn dials 1 to 6 horizontal, using the standard solution (first move is dial 2).  

b.  Slide out the base as far as it will go.  
c.  You can now turn dial 1 vertical again, and then give dials 2, 3, and 4 a half turn each.  
d.  Slide the base back in until dial 5 is at the spot in the frame where it can be turned.  
e.  Give dials 5 and 6 a half turn. Now dial 7 can also be turned horizontal, and the puzzle is solved. 
This shortcut uses L_{6}+7 = 42+7 = 49 moves instead of the
usual 85. It can come in very handy if you started with the wrong move, ending up much further
away from the solved position with six horizontal dials.
The Elephant Spinout has a slightly shorter frame, and you can apply this shortcut
technique a little more easily since you only need to solve dials 15 in step a.
This leads to a solution of L_{5}+7=28 moves.
There is a cheap Taiwanese version (with dials of different colours) which is even shorter
and needs only L_{4}+7=17 moves!