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Question 1154406: An addy number is a five digit number with these properties.
The first leftmost digit plus the second digit equals the third digit
The second digit plus the third digit equals the fourth digit
The third digit and the fourth digit equals to the fifth digit (rightmost)
All digits are different.
If so how many Addy numbers are possible
Found 2 solutions by greenestamps, Edwin McCravy:
Answer by greenestamps(13200)   (Show Source):
You can put this solution on YOUR website!
There is no mathematics we can show you that will help you with this. Get some mental exercise by working the problem yourself.
Obviously the choice of the first two digits determines the whole 5-digit number. So consider all possible first two digits and see which ones produce and addy number.
Suppose, for example, that the first digit is 4. The second can't be 0, because the third would then also be 4, which is not allowed.
So the smallest possible second digit is 1. And that leads to 4156x.
So immediately you know the only possible first digits are 1, 2, and 3. That doesn't lead to many possibilities.
Answer by Edwin McCravy(20060)  (Show Source):
You can put this solution on YOUR website!
Let 1st digit = x
and 2nd digit = y
then 3rd digit = x+y
and 4th digit = x+2y
and 5th digit = 2x+3y
No digit can be 0, since if x or y were 0, then x=y, which is not allowed,
If x=1,
1st digit = 1
2nd digit = y
3rd digit = 1+y
4th digit = 1+2y
5th digit = 2+3y
The 5th digit must be less than 10, so
2+3y < 10
3y < 8
y < 2 2/3, and it can't be 1, so y must be 2
so
1st digit = 1
2nd digit = 2
3rd digit = 3
4th digit = 5
5th digit = 8
So the first addy number is 12358
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If x=2,
1st digit = 2
2nd digit = y
3rd digit = 2+y
4th digit = 2+2y
5th digit = 4+3y
The 5th digit must be less than 10, so
4+3y < 10
3y < 6
y < 2 so y must be 1
so
1st digit = 2
2nd digit = 1
3rd digit = 3
4th digit = 4
5th digit = 7
So the second addy number is 12358
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If x=3,
1st digit = 3
2nd digit = y
3rd digit = 3+y
4th digit = 3+2y
5th digit = 6+3y
The 5th digit must be less than 10, so
6+3y < 10
3y < 4
y < 1 1/3 so y must be 1
so
1st digit = 3
2nd digit = 1
3rd digit = 4
4th digit = 5
5th digit = 9
So the third addy number is 31459
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We have them all, because if x=4, the 5th digit, 2x+3y, would be at
least 11, since y cannot be 0, and 11 is not a digit.
So there are only 3 addy numbers:
12358
21347
31459
Edwin
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