Motorola M500 Manuel d'utilisateur Page 20

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Page 18 M500 180
Problem 180.4 Favourite lottery numbers
Chris Pile
You have eight favourite numbers. What is the minimum number of Na-
tional Lottery tickets you need to purchase to guarantee that you win at
least a 5-number prize if six of your favourite numbers are drawn?
In other words, what is the minimum size of L, where L is a set of
6-element subsets of F = a, b, c, d, e, f, g, h such that each 6-element subset
of F contains at least five elements of least one member of L?
What about seven favourite numbers? Or nine, ten, eleven, . . . ?
ADF—Chris also sent an advertisement which suggests that the answer is
at most 7 tickets for 9 favourite numbers, 14 for 10 numbers and 22 for 11
numbers. The ad even goes on to say that if you are willing to part with
some money, you can acquire the actual plans that tell you to how to buy
the lottery tickets.
Problem 180.5 Triangular tiles
Barbara Lee
A cardboard square of side 2 cm is
thrown at random on to a floor tiled
with a triangular pattern, right.
The side of the large triangle is
20 cm and the side of each small tri-
angle is 10 cm. What is the proba-
bility that the square will not land
on any of the lines where the tiles
join? Assume this pattern repeats
over a large area of floor and all the
tiles are equilateral triangles.
Two mathematicians were having a discussion in a pub about the general
awareness and level of knowledge of mathematics amongst the general pub-
lic. Bill thought that this awareness was pretty good but Ben thought
otherwise. When Ben went to the bathroom, Bill called the barmaid over
and said to her, “When my friend comes back, I’ll call you over and ask
you a question. No matter what I say, you reply ‘one third of x cubed’.”
The barmaid repeated this a couple of times to make sure she got it right,
then she went about her business. When Ben returned, Bill offered to test
his theory and he called the barmaid over. He said to her, “What is the
integral of x squared?” “One third of x cubed,” came the reply, and after
a short pause she added, “plus a constant.” [Sent by Peter Gibbs.]
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