What is the number?

[Guest]

I am looking for a number consisting of 9 digits such that the digits from 1 to 9 appears only once. The number is divisible by 9, but when the right most digit is removed, the remaining number is divisible by 8. Again, when the right most digit is removed, the remaining number is divisible by 7. This property is maintained until the last remaining number of one digit which is divisible by 1.

What is the original 9-digit number?

381654729

[Guest]

All numbers 1-9 are divisible by all numbers 1-9, except you won't always get a whole number as the answer. I assumed that you meant when the division was done, the result had to be a whole number.

I was suprised to find only 1. I thought at least a couple could satisfy the definition.

381654729

[bonanova]

Many impossible combinations can be eliminated from the given conditions:

Since the digit 0 is not present, the 5th digit must be 5.

The odd digit places then are 1 3 7 9 in some order because

the even digit places must be even - 2 4 6 8 in some order.

Each group of 3 digits must be a multiple of 3, meaning their digits sum to 3, 6, or 9.

All combinations of digits 1-9 are divisible by 9.

That takes care of dividing by 9, 5, 3, 2, and 1.

The only divisors that must be checked are 8, 7, 6 and 4.

For the middle three digits to sum to a multiple of 3 they

must be [258] or [456] - where [abc] stands for either abc or cba.

So the possibilities to check are

[147] [258] [369]

[369] [258] [147]

[129] [456] [387]

[387] [456] [129]

[183] [456] [729]

[729] [456] [183]

Dividing the first seven digits by 7 eliminates almost all of these,

and dividing the first 6 digits by 6 brings it down to only one,

which also turns out to satisfy 8 and 4.

381 654 729

[Guest]

Instead of editing your original post to include the answer later on, just add a post to the end.

[Guest]

I actually learned about this number last week.... I'm taking a course on number theory it's called a delectable number. It's sort of useless.

381654729

does anyone know what other type of number this is?

it's a pair of numbers

[Guest]

921654387

963258147

[bonanova]

921654387

963258147

In neither case are the first 8 digits divisible by 8.

They both have a remainder of 6.

[Guest]

What about: 987654321

[Guest]

I am looking for a number consisting of 9 digits such that the digits from 1 to 9 appears only once. The number is divisible by 9, but when the right most digit is removed, the remaining number is divisible by 8. Again, when the right most digit is removed, the remaining number is divisible by 7. This property is maintained until the last remaining number of one digit which is divisible by 1.

What is the original 9-digit number?

381654729

would, not, the answer be 123456789???? 9 is disivible by 8, 8 is divisible by 8..and so on...

[Guest]

All numbers can be divided by numbers 1 to 9, but are not all divisible.

The definition of the mathematical term divisible is where the dividend divided by the divisor has no remainder, i.e., the divisor and quotient are both integers. The confusion might arise in that a divisor, in regards to the operation of division, is not necessarily an integer; yet when one speaks of the divisor of a number outside of the operation itself, a divisor is defined as an integer.

bonanova offers a decent explanation on how one can arrive at the solution.