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10:38
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Q: How many four digits numbers are there not containing zero and multiplication of its digits divisible by 7?

leonardI saw a question in my math book, it seems very trivial, it says that: How many four digits numbers are there not containing zero and multiplication of its digits divisible by 7? I thought of: (all four digits numbers not containing zero) minus (all four digits numbers not containing 7 and 0) i...

Yes your solution is right. Are you sure of the statement?
Well there must be a mistake somewhere. Because your answer is right, I have even checked with Python. And one can easily show that the product of $A$'s digits is divisible by $7$ iff at least one of the digit is $7$.
In fact there are $4904$ four digits numbers such that the product of their digits is divisible by 7. Maybe there is a mistake in your math book.
@Axel I guess you meant not divisible by 7 in your last comment?
@Manan No, why?
@Axel Isn't that precisely the claim that the math book makes- that the number of 4 digit numbers such that their product of digits is divisible by 7 is 4904? I believe the number of 4 digit numbers, not including 0 as a digit, not divisible by 7 is 4904.
Ah, I see what you meant; so you're including all the $4$ digit numbers, even those including $0$ when you accounted $4904$.
Yes precisely !
10:40
I see. Then it most certainly is (1) Imprecise phrasing/solution in the book, or (2) Imprecise phrasing by the asker
Yes, that is what I think too.
You could add your calculations as a final answer which can be accepted.
That is what I am doing. Maybe I'll let some room for the asker to do the calculations by himself.
Morevover, how do you create such text chats? Is it automatic?
I guess the site suggests to move extended discussions to chat. For other chat-rooms(such as CURED and the likes), I'm not aware of the process.
Ok thank you. No problem.
10:45
:)
Ah, I found out
By clicking on the image profile here, you can create a new chat-room with a user.
Alright, thank you!
10:58
Well have a nice day, all of you.
And don't hesitate sending a message if I made a mistake or a typo.

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