326 Answers to assignments
current system. The simplest ways
to do this are by adding 4, 5 or 6 to
the fourth digit (because currently
the fourth digit will always be 0, 1,
2 or 3, so digits 4–9 would clearly
denote foreign-born licence holders)
or adding 2 or 3 to the second digit
(in the current scheme this number
could only be 0, 1, 5 or 6).
Another, more complicated, method
would be to add a number between
31 and 69 (inclusive) to the date
(fourth and fifth digits), as this could
otherwise only lie between 01 and- Any unambiguous and consistent
method would be acceptable as an
answer.
d This question requires you to show
how the number system can be
used in a practical way. As almost
all parents are at least ten years
older, the deception is certain to be
noticed. Your answer should express
the probability as certain. If you
state that it is a high probability, you
should also explain your answer – a
parent will almost definitely be more
than ten years older than their
child – to get the mark.
e Excluding the digits denoting the
year, there are 10,000 possible
numbers (0000-9999), of which
only 365 (or 366 in a leap year) are
valid. So (10,000 – 365) ÷ 10,000
= 96.35%. A good approximation
would be acceptable. One simple
error, for example using 9999 instead
of 10,000 or trying to incorporate
a factor for a wrong year would
normally lose only some of the
available marks.
2 The Fastrack bus leaves Aaland at 8 a.m.,
so passes through the three villages at
8.10, 8.20 and 8.30, arriving at Matsberg
at 8.40. The Stagebus leaves Matsberg
at 7.45 and takes 1 hour 15 minutes,
including three 5-minute stops, so takes
all that they do in captivity. They may
enjoy it, but it is not necessary for the
argument that they do.4, 5 Variable responses5.1 Combining skills – using
imagination
1 a (i) The last two digits of the year are
split – into first and last (sixth)
position, with the month in
second and third and the day in
fourth and fifth. 17 March 1981
(170381) would appear as 803171.
(ii) Each had a repeated digit (two
zeros) so from only one of the
numbers they could not be sure
which one was moved to which
position. Because the repeats are
in different places for the two
people, a pattern can be found
by comparing the two numbers.
(iii) Any date where all the six digits are
distinct is necessary and sufficient:
e.g. 23 Jan 1945 or 17 March 1982.
A number such as 11 November
1911 is a special case. It would
allow the particular birth date to
be predicted, but would not give
the general pattern.
b This introduces a new factor: the
distinction between male and female
numbers, which adds a level of
complexity.
(i) 662126 would give the month
as 62, and 752232 the month as
52, so a five must be added to the
tens of the month (the second
digit of the six) for female drivers.
(ii) Jocelyn was born on 23 February
1972.
c This question requires you to generate
your own method for distinguishing
between different groups. To keep
all the existing information, the
new system would need to use
values which cannot exist using the