A gambler bets half the money in his pocket on the toss of a coin,
winning an equal amount for a head and losing his money if the
result is a tail. After 2n plays he has won exactly n times. Has he
more money than he started with?
You have two bags, four red balls and four white balls. You must
put all the balls in the bags although you are allowed to have one
bag empty. How should you distribute the balls between the two bags
so as to make the probability of choosing a red ball as small as
possible and what will the probability be in that case?
To win on a scratch card you have to uncover three numbers that add
up to more than fifteen. What is the probability of winning a
Published June 2008,February 2011.
Computer simulations exist, but do they provide a genuine 'feel'
for the fall of the dice, and what experience do pupils have of
throws of two or three dice?
We still talk about 'Luck' in getting advantageous results when
throwing dice. Pupils can make up a double-entry dice table for two
dice (e.g. red die along the top and blue die along the side). This
can be used to explain the number of possible combinations for
particular throws from 2 to 12. How would you construct a table for
What activities exist in other cultures (Asian, Chinese, etc.)
where dice or other objects are used for making choices in rituals
In Primary school dice are often marked with numbers or
arithmetic operations and used for specially designed board games.
What opportunities are there for using more than one die?
Dice can be made in the shapes of the Platonic solids. Consider
the odds for different polyhedral dice.
Count the number of throws for three dice as shown in the table
in the poem De Vetula.
Notice that the written numerals on the left give a different
number of throws. Compare this with Galileo's table of results. How
do pupils explain the difference in these results?
3 x 3 Magic Squares are well known in school, but do we ever
investigate higher order magic squares? Make a list of the
line-totals (34, 65, 111, ...) of the magic squares up to the
'Square of the Moon'. Now make a difference table for this list.
What do you notice? How can you explain the result? Now investigate
the sums of all the numbers in each Magic Square.