# Counting problem social security numbers

• cragar
In summary, a social security number is a 9 digit number with the first digit possibly being 0. There are 10^9 numbers available, with half of them being even and half having all even digits. There are 10*10*10*10*10*1*1*1*1 or 10^5 numbers that read the same forward and backward. 9^9 numbers have none of their digits equal to 8, while 10^9 - 9^9 have at least one digit equal to 8. There are 99 numbers with exactly one 8, as any of the 9 slots can have the 8.
cragar

## Homework Statement

social security number is a 9 digit number.
the first digit may be 0
a. How many numbers are available
b. How many are even
c. How many have all of their digits even
d. How many read the same forward and backward
e. How many have none of their digits equal to 8
f. How many have at least one digit equal to 8
g. How many have exactly one 8.

## The Attempt at a Solution

a. assuming we can have a number with all zero's i would say
$10^9$ because we have 10 possible choices for each of the 9 slots
b. I would assume half of part a
c. I would assume half unless there is some kind of fence post error.
d. I think it is 10*10*10*10*10*1*1*1*1
The middle number can be what-ever since its in the middle
so i have 10 choices for that. And the four numbers to the left of the middle can be anything so i have 10 choices for those but this restricts the numbers on the right so I have only 1 choice or those.
e. Since i have removed a possible choice I only have 9 choice for my 9 slots so it should be $9^9$
f. this should be $10^8$ because on one of them I only have one choice but the rest I have 10 choices.
g. On one of the slots I have one choice because it hast to be an 8 , but the rest can't have an 8 in them therefore I have 9 choices on the remaining 8 digits so the answer should be $9^8$

cragar said:

## Homework Statement

social security number is a 9 digit number.
the first digit may be 0
a. How many numbers are available
b. How many are even
c. How many have all of their digits even
d. How many read the same forward and backward
e. How many have none of their digits equal to 8
f. How many have at least one digit equal to 8
g. How many have exactly one 8.

## The Attempt at a Solution

a. assuming we can have a number with all zero's i would say
$10^9$ because we have 10 possible choices for each of the 9 slots
Right.
cragar said:
b. I would assume half of part a
You should write this as a number.
cragar said:
c. I would assume half unless there is some kind of fence post error.
I don't think so. How many choices are there for each of the slots? Is this number half of 109?
cragar said:
d. I think it is 10*10*10*10*10*1*1*1*1
The middle number can be what-ever since its in the middle
so i have 10 choices for that. And the four numbers to the left of the middle can be anything so i have 10 choices for those but this restricts the numbers on the right so I have only 1 choice or those.
Looks good, but you should simplify this number.
cragar said:
e. Since i have removed a possible choice I only have 9 choice for my 9 slots so it should be $9^9$
OK
cragar said:
f. this should be $10^8$ because on one of them I only have one choice but the rest I have 10 choices.
This one bothered me a little, but I think you're right.
cragar said:
g. On one of the slots I have one choice because it hast to be an 8 , but the rest can't have an 8 in them therefore I have 9 choices on the remaining 8 digits so the answer should be $9^8$
OK

and on part c. it should be $5^9$ because I have 5 even numbers to choose from on each slot.
and why does part f bother you.

cragar said:
and on part c. it should be $5^9$ because I have 5 even numbers to choose from on each slot.
Which is quite a bit different from your first answer of .5 * 10^9
cragar said:
and why does part f bother you.
I was concerned that you were counting too many numbers.

ya i think i read part c to quickly . thanks for you help .

Now I think part f is wrong. Because all the ones that have at least one 8 should be the total numbers of possible social security numbers minus the ones that don't have any 8's
so i think the answer to f should be $10^9-9^9$
And now I am not so sure about g . Because if I had an 8 in the first slot I would have one choice then 9 choices for the following, Then I would have to do another chart with an 8 in the second slot and then keep going down the line.

cragar said:
Now I think part f is wrong. Because all the ones that have at least one 8 should be the total numbers of possible social security numbers minus the ones that don't have any 8's
so i think the answer to f should be $10^9-9^9$
And now I am not so sure about g . Because if I had an 8 in the first slot I would have one choice then 9 choices for the following, Then I would have to do another chart with an 8 in the second slot and then keep going down the line.

That's what I got for part f (612579511). For g I got the same thing as e (99). At first this seemed wrong but I think it is right. As you said, 98 is how many possibilities will have an 8 in (only) the first slot. All you have to do is recognize that any of the slots could be the one with the 8 and thus multiple that by the number of slots, so 98 * 9 = 99

## What is the "Counting problem" in relation to social security numbers?

The "Counting problem" refers to the issue of determining the total number of possible social security numbers that can be generated. This is a statistical and mathematical problem that arises from the structure and format of social security numbers.

## Why is the "Counting problem" important?

The "Counting problem" is important because it impacts the security and integrity of social security numbers. If the total number of possible social security numbers is known, it becomes easier to guess or generate valid social security numbers, which can lead to identity theft and fraud.

## What is the current solution to the "Counting problem"?

The current solution to the "Counting problem" is the use of randomization and complex algorithms to generate social security numbers. This makes it difficult for individuals to guess or generate valid social security numbers, thus increasing security.

## Can the "Counting problem" be solved?

Yes, the "Counting problem" can be solved using mathematical and statistical methods. However, due to the constantly changing nature of social security numbers, it is an ongoing problem that requires continuous updates and improvements.

## How does the "Counting problem" affect individuals?

The "Counting problem" can affect individuals by making their social security numbers more vulnerable to fraud and identity theft. It is important for individuals to protect their social security numbers and be cautious when sharing them, as the total number of possible social security numbers is limited.

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