Peculiar Number
The number 381654729 is known for a special property.
If you take pieces of it from left, the number piece will be divisible by its size. Like, 381 is divisible by 3, 38165 by 5 and so on.
That is known to many.
But a question that arises is whether it is unique or whether there is another 9 digit number (lesser size, many are there).
How to get a proof for the uniqueness or a counter-example?
Well one, rather cumbersome way is to check by enumeration. Means, test all the numbers.
We need not test all the 9 digit numbers. We know certain things for sure, like,
5 has to be in the middle.
second digit has to be 2,4,6 or 8.
4th digit has to be 2 or 6 if 3rd digit is odd; otherwise it has to be 4 or 8.
6th digit needs to be even.
and so on.
If you take pieces of it from left, the number piece will be divisible by its size. Like, 381 is divisible by 3, 38165 by 5 and so on.
That is known to many.
But a question that arises is whether it is unique or whether there is another 9 digit number (lesser size, many are there).
How to get a proof for the uniqueness or a counter-example?
Well one, rather cumbersome way is to check by enumeration. Means, test all the numbers.
We need not test all the 9 digit numbers. We know certain things for sure, like,
5 has to be in the middle.
second digit has to be 2,4,6 or 8.
4th digit has to be 2 or 6 if 3rd digit is odd; otherwise it has to be 4 or 8.
6th digit needs to be even.
and so on.
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