Cat's Cradle

Contributed by Michael Bourne (diverti@globalnet.co.uk) cat's cradle layout

Layout

From the top of a 52-card pack, lay out sixteen cards in a square formation, four by four, setting out the cards from left to right and from top to bottom. The remaining 36 cards form the stock.

This layout is made up of a total of eighteen straight lines (marked red in the diagram): four horizontal lines, four vertical lines and two diagonal lines, each of these ten lines containing four cards; four diagonal lines of three cards; and four diagonal lines of two cards.

Aim of the Game

To use up all the remaining 36 cards in the stock.

Rules and Method of Play

i. Only one card can be moved at any one time. This card may be either a singleton or a top card or subsequently revealed card in a stack.

ii. A card may be moved only on to a card which is opposite in colour and of one higher rank, (e.g. Kspade on Adiamond, Aheart on 2club).

iii. A card may be moved only on to a card that is also positioned on one of the same vertical, horizontal or diagonal lines indicated above, but it may be moved in any direction along these lines. A card may not be moved into a space.

iv. During a sequence of play, a card may be moved more than once provided that it is via a card of opposite colour and of one rank higher, and on to a card of the same colour and rank. (See iii. in the example, below.) This kind of move is quite common. It enables a card to reach other lines and to bring into play other cards in the layout.

v. A sequence of play consists of moving around those cards that can be moved and creating spaces in the layout. In the process, stacks of cards are built up. When a player reaches the point of being unable to create any more spaces, the new spaces in the layout are filled in with unseen cards from the top of the stock. After the spaces have been filled in from left to right and top to bottom, the next sequence of play commences.

The game continues until no spaces can be created during a sequence of play, or all 36 cards from the stock have been successfully played.

(Remember that the more spaces you are able to create in a sequence of play, the more cards you will use up from the stock. The ability to create as many spaces as possible will increase with experience and the application of the techniques set out below.)

Example of a sequence of play for this initial layout.

Jclub9spade8heart3club
QheartAspade9diamond9club
7heartQspade2heart2spade
4diamond4heart6club6diamond

i. A move with no option. Jclub on Qheart.

ii. A move with an option. There is a choice to be made with the 8heart which may be placed on the either the 9spade or 9club. (Tactically, with the 6diamond being in a favourable position, the 9club would be preferable.)

iii. A move involving a transfer. The 3club, having been moved on to the 4diamond, may now be transferred on to the 4heart. This now enables first, the 2heart to be moved on to the 3club, and second, the Aspade to be moved on to the 2heart, so that a four card stack Aspade, 2heart, 3club and 4heart is formed.

In this sequence of play, five spaces have been created.

Further examples of the method of play and the way in which cards may be moved around are contained in:-

Playing Hints and Techniques

By applying the following, various techniques and tactics, the chances of success are greatly increased.

  1. To get a better view of any lines of play that require a bit of thought, identify and play first those cards for which there are no optional moves.

  2. When options occur, it is usually better to clear cards from the four central positions, (see EXAMPLE, below). These positions command more lines in the layout. Alternatively, since these four positions are also more likely to receive cards, occasions arise when it may be preferable to use them as bases on which to build stacks of cards in large numbers.
    EXAMPLE(x denotes cards of no consequence.)
    8heart3diamond4clubx
    x3heart10diamondx
    9clubxxx
    xx9spade8diamond
    1.. 3heart on 4club (rather than 3diamond on 4club), but,
    2.. 8heart on 9club, 9spade on 10diamond (rather than 8diamond on 9spade), to avoid "blocking", (see below).

  3. Blocking. When two stacks of cards are each topped by two cards of the same colour and rank, those two stacks become blocked in as much that the top cards cannot now be released, although cards may still be moved on to them. If blocking is unavoidable, it is usually better to have two blocked stacks on the same line, if possible, so that they act together and allow for possible transfers of future cards. In the completed sequence of play in EXAMPLE 5 below, blocking occurs with the Aheart and Adiamond. However, both cards are co-operating together on the same line, ready to receive a black king and allow it to be transferred from one ace to the other and thence, perhaps, to pick up a red queen.

  4. Watch out for opportunities of making use of a card for other purposes before moving it. These occur frequently.
    EXAMPLExxJclubx
    xxxJspade
    Qheartxxx
    xx10heartx
    10heart on Jclub and transfer on to Jspade; then Jclub on Qheart.

  5. Some layouts, at first sight, would appear to offer no possibilities of a move. Take a good look before giving up.
    EXAMPLEx2spadex10club
    JdiamondxxAheart
    xxxx
    10spade/JheartAdiamond/2clubxQspade
    In this sequence, the moves are a. Adiamond on 2spade, Aheart on 2club, (although this unfortunately creates two blocked stacks), and b., not 10spade on Jdiamond, 10club on Jheart, in the same way, as in a), but 10spade on Jdiamond, Jheart on Qspade, 10club on Jheart for three spaces in total.

  6. Complicated configurations of cards often turn up. Care must be taken to work out the best line of play in order to create the greatest number of spaces. The best line of play can be assessed by studying, for a while, the cards in the layout. Here are a couple of not too complicated examples:
    EXAMPLE I.2heart3clubxx
    x2diamondxAspade
    xxxKheart
    xxxx
    It is simple enough to play 2diamond on 3club and Kheart on Aspade for two spaces, but the best line of play is Aspade on 2diamond and transfer on to 2heart, 2diamond on 3club, Aspade on 2diamond, Kheart on Aspade, creating three spaces and still clearing a central position.
    EXAMPLE II.8diamondxx6diamond/7spade
    7club/8heart5spade/4heart6heart/5clubx
    x9spade4diamond3spade
    xxxx
    An inexperienced player might play 4diamond on 5club, 3spade on 4diamond and leave it at that. Perhaps with a little more experience, 7club on 8diamond, 8heart on 9spade, would be spotted, and even 6diamond on 7club, 7spade on 8heart, so as to create four spaces. The best line of play, however, is 4heart on 5club, 3spade on 4heart, 7club on 8diamond, 8heart on 9spade, 6diamond on 7club, 7spade on 8heart, 5spade on 6diamond, 4diamond on 5spade - giving five spaces.

  7. Clearing a stack to create a space. Clearing a stack of two cards is common, three occurs occasionally, but four is quite rare. Opportunities to clear stacks of three and four need to be looked out for. (Remember, only one card at a time may be moved.)
    EXAMPLEx7clubxx
    xx8heart/7spade/6diamond/5spadex
    xxx9spade
    8diamondx6heartx
    5spade on 6heart, 6diamond on 7club, 7spade on 8diamond, 8heart on 9spade, creates one space - and a lifeline if, at first, the game had appeared to have come to an end.

  8. Optional Moves and Preparation. In this layout there is the option of moving Aheart on to 2club or 2spade:
    x2spadexx
    xAheartxQdiamond
    xx10heartx
    Jspadexx2club
    Here, Aheart on 2club is a far better move and prepares for the eventuality of Kspade or Kclub turning up in a succeeding sequence of play so as to enable Qdiamond, Jspade and 10heart to be picked up.

In addition to the above, there are a number of advanced techniques and finer points of play. Some of these are to do with controlling lines of play, calculations based on cards that have yet to emerge from the stock, (8, above, partly comes into this category), and targeting certain spaces for certain cards. The more the game is played, the more players will come to realise and appreciate the skill factors involved. Certainly, Cat’s Cradle can throw up many intricate and challenging sequences for players to solve.

Some statistics based on thousands of games played.

  • Longest winning sequence - 11.
  • Longest losing sequence - about 17.
  • Most number of spaces created at the end of a successful game - 9 (at least six times).
  • Chances of not being able to make a move on the first layout - very, very low, probably about a 200-1 chance.
  • Chances of a successful conclusion - on average, about one in eight for a beginner; for an experienced and skilled player - about one in five.

Copyright © Michael Bourne, divertimenti (UK) 1986 & 1999.

Enjoy the game. Comments and enquiries welcome.

MICHAEL BOURNE, (current C.C. world champion), diverti@globalnet.co.uk