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Start with any number of counters in any number of piles. 2 players take it in turns to remove any number of counters from a single pile. The loser is the player who takes the last counter.

FEMTO: Follow Up

Follow-up to the February Game Rules of FEMTO.

Yih or Luk Tsut K'i or Three Men's Morris

Some puzzles requiring no knowledge of knot theory, just a careful inspection of the patterns. A glimpse of the classification of knots and a little about prime knots, crossing numbers and knot arithmetic.


Age 14 to 16
Challenge Level

There is a book of mathematical games I'm rather fond of, even though it never made the best-seller lists. We called it "What's My Game?", and included in it was a two-player cardgame called Divide and Conquer for which the entire equipment is a single suit of playing cards. This seemed to me to be just about the most minimal cardgame anyone could devise - until I discovered Pico, which is a German cardgame using just 11 cards.

In case anyone think Pico is still just a little too big I've put together ideas from both these games and come up with a new one, called Femto, which needs just eight cards.

Although the game is so small there are plenty of interesting things to be discovered in Femto, so I hope lots of people get in touch with their observations.

Rules for FEMTO

  1. Femto is a cardgame for two players; a Femto pack consists of eight cards numbered 2,3,4,5,6,7,8,10.
  2. The cards are shuffled and dealt, so each player gets four cards.
  3. In each round of play each player puts out one card, face down. The two cards are then turned face up.
  4. The round is won by the higher value card, unless the higher card is more than twice the value of the lower, in which case the lower card wins. e.g. 10 beats 8, 6 beats 5, 3 beats 10, 10 beats 5, ...
  5. Whoever played the winning card chooses one of the two cards and puts it, face up, on the table in front of him/her. The player of the losing card takes the remaining card and puts it back into his/her hand.
  6. More rounds are played until one player has no cards left.
  7. The winner is the player with the greater total value of cards in front of them at the end of the hand.

Well, for a tiny game there seem to be plenty of questions to explore. How long do games last? What is a typical winning score? How many different hands are possible? Which cards are the most powerful? Indeed, what is the most powerful hand (and how could it be beaten)?

Then there's another set of questions, and as a game developer these are the ones which particularly interest me. The first version of any game is often interesting enough but needs a bit of tinkering to turn it into the finished version. Perhaps the most obvious question to ask is whether we've got the right set of cards. To take another set almost at random, would 5,7,9,13,16,18,20,24 be any better? Or perhaps we should stick with the original set but add a 12: deal out four cards each so that one card is left unused. Or perhaps there's a role for a Joker card.

Other questions which I'd want to explore concern the game structure. I've suggested that the cards are dealt out, but what if the players take turns to choose cards to make up their starting hand? And instead of playing simultaneously, what if each round is played with one player leading a card face up, so that the second player can see its value before responding? I've also got a hankering to change rule (5), so that it's the losing player who chooses which card goes back into his/her hand. Or perhaps it should be not the winner or loser of the individual round who chooses, but whoever is currently winning (or perhaps losing), who makes the choice, ....

Changing the overall winning criterion often has interesting consequences. The most usual way to do this is to make the winner the person with the lower score rather than the higher. Or in this case, the aim might be to score an odd total, or a total that is a multiple of 3, or a prime number, ....

So it's not true after all that Femto is a game. It's more accurate to say that it may become any one of dozens of potential games. (If there's actually too much choice perhaps we'd be better off looking for a still smaller game, Atto?) I don't know how Femto will end up, but I am excited by the possibility of lots of people trying out different versions, especially the prospect that they might share the development, including playing different versions, by Internet or e-mail.

Do please let me know how you get on. I'll offer a prize (a copy of "What's My Game?" of course) to the best and most interesting commentary and final version, and I'll be looking forward to hearing from you.

Alan Parr


A follow-up on Femto can be found here.