Copyright © University of Cambridge. All rights reserved.
Let's play a game
I have a large set of cards which are printed 'Poison', 'Antidote'
I shuffle up the cards and lay out a row of 5 cards, face
You choose any two cards which are next to each other and turn them
over. Two Poison cards is still Poison, so replace these two cards
with a single Poison card. The same goes for two Antidote or Water
cards - replace two of these with a single Antidote or Water card
respectively. Mixing Water with Poison still leaves Poison,
and mixing water with Antidote still leaves Antidote (we ignore the
chemistry of concentrations in this game!)
The game is to repeat this procedure until you are left with a
single card, and you lose if you end up with Poison.
My question is
: Does the order in which you decide to turn over
the cards Sometimes, Always or Never matter? Give examples or a
clear argument to illustrate your conclusion. If the cards are
totally random, what is the chance of me being Poisoned?
You can play with this interactivity if you wish:
If you can see this message Flash may not be working in your browser
Please see http://nrich.maths.org/techhelp/#flash to enable it.
Hopefully you survived the game of Poison, Antidote Water! Now
let's play a similar game based on the classic Scissors, Paper,
Stone. In this game Scissors beats Paper, Paper beats Stone and
Stone beats Scissors.
I lay out face down a row of 5 cards printed with one of these
symbols and you turn over two cards next to each other, replacing
it with the winner of the two cards if the two cards are different
or removing one of the two cards if they are the same.
My question is again this
Does the order in which you decide to turn over the cards
Sometimes, Always or Never matter? Give examples or a clear
argument to illustrate your conclusion.
Now consider this
: What are
the structural similarities and differences between the two
you are given a set of cards with 3 different images on them (you
choose!). Is it possible to invent a different set of rules
such that the order in which the cards are turned over does not
affect the result of the game?
Repeat for a
game with sets of cards with 4 images on them.