318 Answers to assignments
3.6 Solving problems by searching
1 There are a large number of ways of
paying, but clearly 1 adult + 1 senior
citizen + 2 children (total $32) comes
to more than the family ticket ($30), so
some combination using a family ticket
must be used.
Family ticket ($30)
+ 2 extra children ($10)
= $40
Single-adult family ticket ($20)
+ extra senior citizen ($5)
+ 2 extra children ($10)
= $35.
The latter is the best option.
2 The options to search involve dividing
the books as: 7, 5 + 2 or 4 + 3. (6 + 1
would be silly.) The prices, respectively,
are $3.20, $2.15 and $2.10. The last of
these is the best.
3 One can start listing the piles
systematically:
20 × 5¢
16 × 5¢ + 1 × 20¢
12 × 5¢ + 2 × 20¢
continuing to 5 × 20¢; thus there are
piles containing 0 to 5 × 20¢ coins, or 6
piles in total.
4 a There are two ways to approach this:
to list all possible scores, and to look
at the make-up of the scores listed.
The first is probably safer, but more
time-consuming.
28 is 6 correct and 1 wrong:
(6 × 5) – (1 × 2)
18 is 4 correct, 1 wrong and 2
unanswered: (4 × 5) – (1 × 2) + (2 × 0)
16 is 4 correct, 2 wrong and 1
unanswered: (4 × 5) – (2 × 2) + (1 × 0)
12 cannot be done
−1 is 1 correct, 3 wrong and 3
unanswered: (1 × 5) – (3 × 2) + (3 × 0).
So the Kool Kats score is incorrect.the diagram. So the number of links is
1 + (33. 2 1.2)
0.8− = 41
The 26.2 cm length would be 25.2 cm
without the end fitting, so the number of
links is
1 + (25. 2 1.2)
0.8− = 31
The total number of links is 72.
2 The plane’s velocity from Los Angeles to
Mumbai is 14,000 22 km/hr (636 km/hr).
From Mumbai to Los Angeles it is
14,000
17 km/hr (824 km/hr). The wind
velocity is half the difference (it adds
to the velocity one way and subtracts
in the other),^1882 or 94 km/hr.
3 Lighthouse 1 flashes at 0, 11, 22 etc. seconds
from the beginning. Lighthouse 2 flashes
at 0, 3, 7, 17, 20, 24, 34 etc. It is possible
to list all the flashes of both until we find
a coincidence. Otherwise, we can look at
the various flashes of lighthouse 2. The first
flash repeats every 17, so would coincide
with the 11-second cycle at 187 seconds.
The others are offset by 3 and 7 seconds
from this (i.e. they repeat every multiple of
17 plus 3 and 7; the next ones are at 37 and
41 seconds), so we are looking for a multiple
of 17 which is smaller than a multiple of 11
by 3 or 7. Looking at 17, 34, 51, 68, none
work. However, 85 is 3 less than 88, so the
two lighthouses coincide after 88 seconds.
What is the next coincidence?
4 This appears to be a Venn diagram
problem, and one could be used to solve
it. However, there is an easier analysis.
If we add the number with neither (5)
to the number with a dog (13) and the
number with a panda (12), we get 30.
There are only 23 children in the class,
so the difference (7) must be the overlap,
or those with both a dog and a panda.
You might like to draw a Venn or Carroll
diagram to show all the subdivisions.