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
Investigations based on an Indian game.
All you need for this game is a pack of cards. While you play the
game, think about strategies that will increase your chances of
This is a simple patience which often comes out.
Lay out an array of 12 cards in 3 rows of 4 cards, face up. Use
the remaining cards to cover pairs of cards that sum to 11 (not
including picture cards) and to cover sets of 3 picture cards, a
Jack, Queen and King, which do not have to be the same suit. The
object of the game is to put down all the cards in your hand and
finally to remove all the cards from play. If you can get rid of
all the cards in your hand in this way you can go on to the second
stage of the patience. If however you are left with one card in
your hand you have failed. At this stage you remove from play two
or three whole piles at a time where either the cards on the top
are a pair adding up to 11 or a set of three picture cards. If you
can remove all the piles in this way you have succeeded!
Why should you try to avoid covering one or three sets of
Can you explain why it is, that if you reach the second stage
having used all the cards in your hand, you can always finish the
Investigate the game where you have 8 or 10 cards face up rather
than 12. How does this change the probability of getting the
Make up some rules of your own.