since it is a 5-digit number, we could let 5 variables for this problem.

let a be the ten thousand's digit

b be the thousand's digit

c be the hundred's digit

d be the ten's digit

e be the one's digit

n be the number

with this, we could make a formula out of this:

eq. 1: 10,000a + 1,000b + 100c + 10d + 10e = n

back to the problem, it says that, "my one's digit is 2 less than my ten thousand's " interpreting this given, we could say that:

eq. 2: e = d - 2

" hundred's digit is 1 less than my ten thousand's "

eq. 3: c = a - 1

" my other digits are twice my ones digit,"

the other digit is thousand since it is the only place that it has not been said.

eq. 4: b = 2e

we are asked to find the possible numbers. first, we have to find the limitations on each equation since digits could not be negative.

we don't have a problem on equation 1 and equation 4 since only number that should not be included are less than zero or negative numbers. for equation 2, the one's digit is equivalent to 2 less than the ten's digit meaning the ten's digit should be greater than or equal to 2. lastly for equation 3, the hundred's digit is 1 less than my ten thousand's digit meaning the ten thousand's digit should be greater than or equal to 1.

we could just use listing method.

let's start our ten's digit since it is the first digit in the problem that has restrictions. our possible numbers are 0-9. our ten's should be greater than or equal to 2. so the possible values of our ten's digit are:

d = 2, 3, 4, 5, 6, 7, 8, 9

next, the one's digit. it must be one less than its ten's digit so subtract one from each of the following possible ten's digit:

d e

2 1

3 2

4 3

5 4

6 5

7 6

8 7

9 8

afterwards, the ten thousand's digit, the second digit that has restrictions. ten thousand's digit should be greater than or equal to 1. the possible values are:

a = 1, 2, 3, 4, 5, 6, 7, 8, 9

then, the hundred's digit 1 less than my ten thousand's digit. the possible values are:

a c

1 0

2 1

3 2

4 3

5 4

6 5

7 6

8 7

9 8

lastly, the thousand's digit should be twice the one's digit. the possible values are:

d e b

2 1 2

3 2 4

4 3 6

5 4 8

these numbers down here are impossible so it must be omitted on the possible values.

6 5 -

7 6 -

8 7 -

9 8 -

list of possible values:

a c

1 0

2 1

3 2

4 3

5 4

6 5

7 6

8 7

9 8

d e b

2 1 2

3 2 4

4 3 6

5 4 8

with these values, we must remember that a and c and d, e and b must always correlate and stick together. the following numbers are possible:

12021 22121 32221 42321 52421 62521 72621 82721

14032 24132 34232 44332 54432 64532 74632 84732

16043 26143 36243 46343 56443 66543 76643 86743

18054 28154 38254 48354 58454 68554 78654 88754

92821

94832

96843

98854