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Q: How to solve a Mechanical IQ puzzle (like Tower of Hanoi)? ( No Answer,   4 Comments )
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 Subject: How to solve a Mechanical IQ puzzle (like Tower of Hanoi)? Category: Science > Math Asked by: pkuanko-ga List Price: \$3.00 Posted: 21 Nov 2006 17:46 PST Expires: 21 Dec 2006 17:46 PST Question ID: 784665
 ```This is a puzzle I bought. It has 5 coloured pegs, R(ed), Y(ellow), G(reen), B(lue) and P(purple). Initially on each pegs, there are 4 discs (of SAME size, unlike Hanoi) but of different colours. On the R(ed) peg, in order from top to bottom, the discs are Y, G, B, P. On the Y peg, the discs are G, B, P, R. On the G peg, the discs are B, P, R, Y. On the B peg, the discs are P, R, Y, G. On the P peg, the discs are R, Y, G, B. The aim is to end the game with the 4 discs of each colour on their matching peg subject to the rules: 1. Discs may be moved singly or in pairs. 2. A disc may be moved onto another disc of the same colour or onto an empty peg of that colour. 3. When 2 discs are moved together, the bottom one is the indicator of the colour and can be placed onto a disc or empty peg of the same colour. 4. No more than 7 discs can be stacked on a peg at one time. I've tried this puzzle many times but find it impossible to go far. Can any mathematician confirm that this cannot be solved (I don't need any proofs, just simple "No")? Or if you can provide the solution, I will give you a good tip. Please try this puzzle out and give me your comments!```
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 ```No, the problem appears unsolvable. Even a simplified version of it with only 3 different coloured pegs with 2 different colured discs and similar rules cannot be solved.```
 ```Thank you for your comments. That's why I find this puzzle very puzzling to solve with the given rules. Interestingly, the puzzle came from a box with a "Marks and Spencer" label! Could it be that the inventor simply wrote the instructions without even trying out the puzzle himself, or even bothering whether it could be solved or not?```
 ```Problems of this kind are sometimes easier to work out going in reverse, ie. start with the disks segregated on the pegs of matching colors and see if the "mixed up" state (where disks are taboo on the peg of the same color) can be attained. regards, mathtalk-ga```
 ```I've been working on this puzzle, and I have a couple of observations to add. The final state is homogeneous, with each disk resting on a peg or other disk of the same color, while the initial state is free of such matches. Since a move can result in increasing the number of matches by one and never decreases the number of coloring matches, at least twenty moves are required, possibly (likely) more. The other note is wondering whether as originally worded the move of a pair of disks is allowed to invert the order of the two disks as they are transferred. In working with some smaller versions of the puzzle I find that it cannot be solved without allowing one such move. I wrote a Prolog program to search for solutions, but the depth of the puzzle (20+ moves, some branching) makes it a computational challenge for my laptop! regards, mathtalk-ga```