Doing this problem I noticed something odd:
When we flip the digits of a two digit positive integer, the difference between the new integer and the first one is the result of 9*(difference of the 2 digits):
A difference of 36 by flipping the digits of the integer means that the difference of the 2 digits will be \(36/9=4\).
I have tried it with several combinations and it seems to work, I really can't tell why. Examples:
Difference of the digits = A
Difference between the two integers = B
Say B = 27, then:
\(B = A*9\)
\(A = 27/9 = 3\)
So every combination of digits with a difference of 3 will create two integers with a difference of 27: 30-03, 41-14, 52-25, etc.
Say B = 63, then A would be 7: 70-07, 81-18, 92-29.
In that sence if they tell me that the difference of two integers when their digits are flipped is 54, I can immediately know that the difference of the 2 digits will be 6. IF it is 36, then 4. 81, then 9. ETC.
I think once I grasped this, this type of problems will be much easier.
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