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# Help needed!

How many four digit numbers containing $$\text{NO}$$ zeros have the property that whenever any one of its four digits is removed, the resulting three-digit number is divisible by $$\large{3}$$ ?

Thanks~

Any help appreciated peeps!

Note by Anik Mandal
1 year, 5 months ago

## Comments

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243?

We can easily prove that all the digits must have the same remainder modulo 3, and that any such contruction will satisfy the property.

There are three groups with the same remainder modulo 3, $$(1,4,7) ; (2,5,8) ; (3,6,9)$$. After selecting the group, there are three possible digits to select for four places. Hence the answer is $$3* (3^4) = 243$$ · 1 year, 5 months ago

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did it the same way. this should be correct, i don't see any alternative. · 1 year, 5 months ago

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Nice thinking! I think your answer is right sir. · 1 year, 5 months ago

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Why does everyone call me Sir? I'm still in school -.- · 1 year, 5 months ago

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Comment deleted May 22, 2015

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Even I got the same · 1 year, 5 months ago

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Yep I know. · 1 year, 5 months ago

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Think so...Well what is your method? · 1 year, 5 months ago

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