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Where Roman numerals exist they are replaced by their modern equivalents.
CLICK = 100 50 1 100 K
I = 1
V = 5
X = 10
L = 50
C = 100
D = 500
M = 1000
Puzzle 123
In the following sum the digits 0 to 9 have all been used, O = Odd, E = Even, zero is even and the top row's digits add to 9. Can you determine each digit?
Hint: The largest possible numbers could start with 6 and 8, therefore the first digit of the answer is 1.
Answer:
Remembering that:
E + E = E
O + O = E
E + O = O
To discuss individual letters it's easiest to represent the sum as:
A B C
D E F +

G H I J
The largest values for A and D are 6 and 8, which makes G = 1.
Since column 2 is E + O = O there can be no carry from column 1 (since E + O + 1 is always even). Therefore C and F are 3 and 5 (but we don't yet know which is which), therefore J = 8.
There can't be a carry from column 2 (as A + D is even) therefore E can't be 9 as this would force a carry.
Therefore I = 9. Hence B can't be 0. Therefore H = 0.
The last remaining odd number makes E = 7. Making B = 2.
Therefore A and D are 4 and 6 (but we don't yet know which is which).
Since the top row's digits have to add to 9 the top number must be 423.
This makes the sum 423 + 675 = 1098.
Puzzle 124
A large fresh water reservoir has two types of drainage system. Small pipes and large pipes.
6 large pipes, on their own, can drain the reservoir in 12 hours.
6 small pipes, on their own, can drain the reservoir in 18 hours.
How long will 6 large pipes and 6 small pipes take to drain the reservoir?
Firstly we find a time that both 12 hours and 18 hours would fit in to...
In 36 hours:
6 large pipes can drain 3 reservoirs.
6 small pipes can drain 2 reservoirs.
Therefore, together, 6 large and 6 small pipes can drain 5 reservoirs.
36 hours ÷ 5 = 7.2 hours.
7.2 hours = 7 hours and 12 minutes.
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