Copyright © University of Cambridge. All rights reserved.
'Shapely Pairs' printed from http://nrich.maths.org/
For this challenge, you will need to print out a set of triangle
The first part is a game for two or more players; then there are
some questions you can think about.
This type of game is played with lots of different sorts of cards;
you might have heard it called Pairs, or Pelmanism. To play this
version of the game, shuffle the cards and then lay them face down
on the table, arranged in rows. Players take it in turns to turn
over two cards. If the player can draw a triangle with the two
properties shown, then s/he takes the cards. If not, once all the
players have had a chance to look at the two cards and see where
they belong, the cards are turned back over. Of course it will help
you if you can remember where the cards are! The game finishes when
no matter which two cards are turned over, there is no triangle
with both of those properties. The winner is the person with the
most cards at the end of the game. Good luck!
Now here are some questions to get you thinking. Use the triangle
cards for these.
Suppose instead of having the cards face down we have them all face
up. If it's your turn first, how many possible pairs of cards are
there that you could choose and win (that is, in how many ways
could you choose a pair so that there is a triangle with both the
properties)? Can you list all the possible pairs?
At the end of the game, you might be left with some cards that
can't be paired up. What's the largest number you could be left
with like this? What's the smallest? Give examples for each.
Now suppose that you want to make a pile of cards so that no matter
which two you pick, you can always draw a triangle with both those
properties. How big could the pile be? Can you give an
This problem is based on the
Triangle Property Game from "Geometry Games", a photocopiable
resource produced by Gillian Hatch and available from the
of Teachers of Mathematics