The Missing Link: Ideal's Answer to the Cube

Quick answer: the Missing Link is a 1981 puzzle from Ideal Toy Corporation, invented by Steven P. Hanson and Jeffrey D. Breslow. Four columns of coloured chain tiles wrap a rectangular body; only the top and bottom rows rotate, and one gap lets tiles slide vertically. There are 326,918,592,000 arrangements.

Best for: people who found the Rubik's Cube fiddly but liked the idea of restoring a scrambled pattern.

Ideal had just sold the Rubik's Cube to the world and needed a follow-up. What they produced was not a cube variant, and the reason it is interesting is a restriction rather than a feature.

What Is the Missing Link?

A rectangular handheld puzzle with four sides. Each side shows a chain in its own colour, originally red, green, blue and white. The body is divided into four rows.

Each side holds four tiles, except one, which holds three tiles and a gap. That single empty space is the only room the puzzle has to move in, exactly as in the 15 puzzle.

Solved, each face shows one unbroken colour-coded chain of interlocked links.

What Makes It Different From the Rubik's Cube?

The two middle rows do not rotate. That is the whole design.

The top row and the bottom row turn freely. The two rows between them are frozen in place. Tiles can only enter or leave those middle rows by sliding vertically into the gap.

So the puzzle is a hybrid: part rotation puzzle like the Cube, part sliding puzzle like the 15. Neither set of habits works on its own. To move a tile from the second row to the third you cannot turn anything; you have to loop it up and around through the gap, one position at a time.

That restriction is why the puzzle feels so much slower than a cube. On a cube every piece is always a few turns from anywhere. Here, the middle is nearly sealed.

How Many Arrangements Does It Have?

326,918,592,000. About 327 billion.

Set against the Cube's 43 quintillion that looks almost modest, and the Missing Link is generally reckoned the easier of the two to restore. The number is still far past anything you could search by hand, and the restriction on the middle rows means the useful moves are fewer than the raw count suggests.

How Do You Solve the Missing Link?

By treating the gap as the thing you are actually moving, and by working in the right order.

Solve one column first and protect it. As with most puzzles of this shape, the method is to finish a region and then only use sequences that return it to where it was.

Think of the gap as the tool. Nothing moves vertically except into the empty space, so plan where the gap must be several moves ahead rather than planning where a tile should go. This is the same reorientation that Huarong Dao demands.

Use the top and bottom rows to deliver tiles. Rotating those rows is cheap and costs you nothing in the middle. Bring a tile around to the column holding the gap, then move it vertically. Rotation positions, sliding commits.

Leave the middle rows for last. They are the hardest to reach and the easiest to disturb, so finishing them first guarantees you will wreck them.

Why Did It Not Last Like the Cube?

Partly timing and partly shape.

It arrived in 1981, at the crest of the Rubik boom, as one of a great many puzzles hoping to be the next one. Almost none of them were. The Cube had already taken the cultural position available, and a rectangular keychain-sized object with chain graphics did not displace it.

There is also a quieter reason. The Cube is satisfying to fidget with even when you are not solving it. The Missing Link, with two frozen rows and one gap, is not. It is a better logic puzzle than it is an object to hold, which is a hard way to sell a toy.

What Should You Try Instead?

We make no permutation puzzles at all, so nothing here is a substitute, and the honest version of this section is short.

If the appeal was the sliding half, read sliding block puzzles, which is the family it borrows from. If it was restoring order through a long forced sequence, the puzzles we make that scratch that are Snake Cube, with a walkthrough, and Tower of Hanoi.

The full range is in mechanical puzzles.

Frequently Asked Questions

What is the Missing Link puzzle?

A 1981 puzzle from Ideal Toy Corporation with four sides, each showing a chain in a different colour. The top and bottom rows rotate, one position is an empty gap, and tiles slide vertically into it. Solved, each face shows one unbroken chain.

Who invented the Missing Link?

Steven P. Hanson and Jeffrey D. Breslow. Ideal Toy Corporation produced it in 1981 as a follow-up to the Rubik's Cube.

How do you solve the Missing Link?

Plan around the gap rather than around the tiles, since nothing moves vertically except into the empty space. Use the freely rotating top and bottom rows to bring a tile to the column holding the gap, then slide it. Solve the middle rows last, because they are hardest to reach and easiest to disturb.

Why do the middle rows not rotate?

That is the design. Only the top and bottom rows turn, so tiles can enter or leave the two middle rows only by sliding vertically through the gap. It makes the puzzle a hybrid of a rotation puzzle and a sliding puzzle, and it is the source of nearly all the difficulty.

How many combinations does the Missing Link have?

326,918,592,000, about 327 billion. That is far fewer than the Rubik's Cube's 43 quintillion, and the Missing Link is usually considered the easier of the two to restore.