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Quiz of the Month (April 2001)
Hector C. Parr
***
SOLUTION TO LAST MONTH'S QUIZ
1) 20 mph
2) 37, 51, 60, 65, 87
3) (a) 9 (b) 265
Notes
1). Suppose normal speed = v mph
Then normal time = 5/v hrs.
So 5/(v + 10) = 5/v  1/12
Solving, v = 20 (or v = 30 ! )
2). By intelligent trial and error.
3). The following is a general solution:
Let f(n,m) represent the number of arrangements of
the numbers 1 to n with exactly m in their correct
positions. It is easy to show that
f(n,m) = _{n}C_{m} f(nm,0) (where _{n}C_{m} is the number of
selections of n objects takem m at a time).
This enables the following table to be built one
column at a time, using also the fact that the total
for each column must be factorial n.
n = 1 2 3 4 5 6 (etc)
m = 0 0 1 2 9 44 265
1 1 0 3 8 45 264
2 1 0 6 20 135
3 1 0 10 40
4 1 0 15
5 1 0
6 1
Alternatively, solution by computer is possible.

THIS MONTH'S QUIZ
1. Two oranges and three lemons cost 119 pence. If an
orange costs 7p more than a lemon, what does a
lemon cost?
2. Andrew and Barry together have £29 in their pockets,
Barry and Charles together have £40, while Charles
and David together have £65. David has twice as much
as Andrew. How much has Barry?
3. A wineglass contains 10 cl of wine, and a waterjug
contains 100 cl of water. If 1 cl of water is taken
from the jug and well mixed with the wine, and then
1 cl of the mixture is returned to the waterjug, which
is greater, the volume of water in the wine or wine in
the water?

***
(c) Hector C. Parr (2001)
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