Reasoning
Take the third letter of the first word
+ the second letter of the second word
+ plus the first letter of the first word
+ plus the fourth letter of the second word.
Hint
In order for the clocks to show the same time (e.g. 2 o'clock), what must the total time gained by one, and lost by the other, total?
Answers Midnight, 10 days later, when they will both show 4 o'clock. Midnight, 30 days later, when they will both show 12 o'clock. Reasoning #1
In order for the clocks to show the same time, the total time gained by one, and lost by the other, must be 12 hours.
For example, if the first clock were to show 2 o'clock, it would have gained 2 hours. In order for the second clock to also show 2 o'clock, it would have had to have lost 10 hours. This is a total of 12 hours gained and lost.
We know that for every hour that passes, the first clock gains one minute, and the second clock loses 2 minutes, for a total time gained and lost of 1 + 2 = 3 minutes.
The total time gained and lost will equal 12 hours when 12 x 60 ÷ 3 = 240 hours have passed. 240 hours = 10 days.
The first clock will have gained 240 x 1 minutes = 240 minutes = 4 hours.
The second clock will have lost 240 x 2 minutes = 480 minutes = 8 hours.
So, they will both show 4 o'clock, 10 days later.
Reasoning #2
In the first answer, we can see that 10 days later, the clocks both show 4 o'clock.
If we move forward another 10 days, both clocks would show 8 o'clock.
If we move forward another 10 days, both clocks would show 12 o'clock.
This will now be the correct time.
So, they will both show 12 o'clock, 30 days later.
Hint
The answer is 4 digits long, so what must G equal?
Answer
423 + 675 = 1098.
Reasoning
Remembering that:
even + even = even
odd + odd = even
even + odd = odd
To discuss individual letters, it's easiest to represent the sum as:
A B C
D E F +
————————
G H I J
A + D has to be over 9, which means that G = 1.
B + E = I, is even + odd = odd, which means that we can't have a carry from C + F (otherwise it would have been even + odd + 1, which is even).
The 1 has already gone, so the smallest possible value for either C or F is 3, which means that the other can't be 7 or 9 (otherwise we'd have a carry).
Therefore, C and F are 3 and 5, but we don't know which is which. But we do now know that J = 8.
A + D = H, is even + even = even, which means that we can't have a carry from B + E. Therefore, E can't be 9, as this would force a carry. So E = 7.
I is the only remaining odd number, so I = 9.
Which means that B = 2.
Neither A nor D can be 0 (otherwise we would have two of the same digit). So, H = 0.
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, A can't be 6, so A = 4, making C = 3.
