Question

My Questions is:
An addy number is a 5-digit number with the following properties:
• The first (leftmost) digit plus the second digit is the third digit.
• The second digit plus the third digit is the fourth digit.
• The third digit plus the fourth digit is the fifth (rightmost) digit.
• All of the digits are different.
How many different addy numbers are possible?

Answer 1

Answer:

Three different addy numbers are possible. They are 12358, 21347 and 31459.

Step-by-step explanation:

Let the 1st two digits of the numebr be x and y

Given that, 1st digit = x

2nd digit = y

3rd digit = x + y

4th digit = x + 2y

5th digit = 2x + 3y

None of the diigts can be 0 because then x = y, also none of the digits can be more tan 9 which limits the possible first digits as 1,2 and 3

(i) consider x= 1,hence  2x + 3y < 10

2 + 3y < 10

3y < 8

which makes y < $2\frac{2}{3}$, since y cant be 1, it is 2

sub x = 1, y = 2 we get the number as 12358.

(ii) consider x= 2,hence  2x + 3y < 10

4 + 3y < 10

3y < 6

which makes y < 2,then y becomes 1

sub x = 2, y = 1 we get the number as 21347.

(iii) consider x= 3,hence  2x + 3y < 10

6 + 3y < 10

3y < 4

which makes y < $1\frac{1}{3}$ , then y becomes 1

sub x = 3, y = 1 we get the number as 31459.