# Ring puzzle solutions for the 5-ring mechanical, or Chinese ring puzzles are shown below.

The ring puzzle solutions presented here are actually a variant of the Chinese ring puzzle

( which can be of the order 5, 7, or 10-rings).

It is essentially a mechanical puzzle constructed by taking an elongated enclosed metal loop and

in-twining it in a series of metal rings, which themselves are anchored on a stationary interlocked

ring or anchor(see Diagram 1)

Diagram 1

The goal of this puzzle is to remove the rings from the loop, or the loop from the rings (depending on your preference).To solve this puzzle we must drop or lift the rings through the loop in a specific sequence.Each repositioning of a ring (either up or down) being counted as a single move.

Begin with the ring labeled 1:

drop it down below the loop as shown.

[STEP/MOVE 1]

Repeat this same process with ring 3.

[STEP/MOVE2]

Next pass 1 back up again through the end of the loop.

[STEP/MOVE3]

Now bring down 1 and 2 together ; followed by 5.

(note: 1, 2 and 3 should ALL be down along with 5)

[STEP/MOVE 4,5,6]

At this point move rings 1 and 2 up together again!

[STEP/MOVE 7,8]

Immediately drop ring1 back down again

[STEP/MOVE 9]

Put ring 3 back up

[STEP/MOVE 10]

Yup you guessed it ring 1 goes back up again

(<---Your puzzle should now look like this)

[STEP/MOVE 11]

Drop rings 1 and 2 together (as shown)

[STEP/MOVE 12, 13]

Move ring 4 down now.

[STEP/MOVE 14]

Rings 1 and 2 now go back up together (once more)

[STEP/MOVE 15, 16]

Lets move ring 1 back down again!

[STEP/MOVE 17]

Move ring 3 back down

[STEP/MOVE 18]

Ring 1 is lifted up again

[STEP/MOVE 19]

Now simply slide rings 1 and 2 off the end : Congrats problem solved!!!

[STEP/MOVE 20,21]------21 steps as promised!

.The most interesting thing about the ring puzzle solutions for the Chinese ring is that unlike

many other mechanical puzzles the chinese puzzle rings can be solved without actually

touching the rings.This is the reason I have included it here and we will now show the proof by

mathematical formula to show how this solution requires exactly 21 steps...imagine that!!

Here is the proof:

(The actual formula depends on the # of rings). Without even moving a single ring we can state mathematically, that the number of moves (call it M) is given in terms of the number of loops ( n ) as :

M = ( 2 ^ n+1 - 1) / 3, if the number of loops are odd.

or,

M = ( 2 ^ n+1 - 2) / 3, if the number of loops are even.

So that the ring puzzle solutions for the 7- and 10- ring puzzles can be calculated as follows:

Substituting n=7 we get M= (2^ 8 -1)/3= (grab your calculators lol !)

255/3 = M = 85 MOVES !!!!!

Next if we calculate the value of a chinese ten ring puzzle (that is replacing n =7 , with n=10),

would result in needing to perform a whopping 682 ring moves!

(What a wonderful finger exercise indeed!)

So we can now show off to our friends and expose the mysteries of the chinese ring puzzles

(This just goes to show you the importance of mathematics in providing an absolute proof to the ring puzzle solutions!!)

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