- #1

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We have 5 digit. How many 7-digit numbers can we create that each two of them have at least 2 different digit?

Could you help me?

I think that the answer is 5^6 but don't know how to prove it.

- Thread starter Jurij
- Start date

- #1

- 14

- 1

We have 5 digit. How many 7-digit numbers can we create that each two of them have at least 2 different digit?

Could you help me?

I think that the answer is 5^6 but don't know how to prove it.

- #2

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Could anybody help me? Please, give me at least hint.

- #3

Tom Mattson

Staff Emeritus

Science Advisor

Gold Member

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Let's start with this: Why do you think the answer is 5^{6}?

- #4

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OK.

I don't know if you understand the task. The numbers have to have at least 2 different digit on some position. For example when we have 5 digit: 1, 2, 3, 4, 5, numbers 1234512 and 1234545 or numbers 5555555 and 1551555 are good.

When we have 2-digit numbers we have 5^1=16 numbers and 5 that each two of them have at least 2 different digit.

When we have 3-digit numbers we have 5^3=125 numbers and 5^2=25 that each two of them have at least 2 different digit because each two of 2-digit numbers have at least 1 different digit and when we add third number we get 25.

So for 7-digit numbers we have 5^6.

I don't know if you understand the task. The numbers have to have at least 2 different digit on some position. For example when we have 5 digit: 1, 2, 3, 4, 5, numbers 1234512 and 1234545 or numbers 5555555 and 1551555 are good.

When we have 2-digit numbers we have 5^1=16 numbers and 5 that each two of them have at least 2 different digit.

When we have 3-digit numbers we have 5^3=125 numbers and 5^2=25 that each two of them have at least 2 different digit because each two of 2-digit numbers have at least 1 different digit and when we add third number we get 25.

So for 7-digit numbers we have 5^6.

Last edited:

- #5

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"can we create that each two of them have at least 2 different digit?" ??!??!

- #6

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Yes. you're right. My english isn't very good. But it should be clear now. Could anyone help me?

- #7

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Is there something that you can't understand in the problem or you don't know how to do it?

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