A number is divided by 10 the reminder is 9--the same number is divided by 9 the reminder is 8--the same number is divided by 8 the reminder is 7 ---like this the same number is divided by 7 the reminder is 6--divided by 6 reminder 5--divided by 5 reminder 4--divided by 4 reminder 3--divided by 3 reminder 2 --divided by 2 reminder 1--What is the Number

Piece of cake. Let be the number. Since divided by 10 gives a remainder of 9, then gives a remainder of zero when divided by 10. So is a multiple of ten. Similarly, since divided by 9 gives a remainder of 8, then gives a remainder of zero when divided by 9. And we can continue this for all the numbers from one to ten. So we get:




Now that I think about it, there are an infinite number of possible answers.

would also give a remainder of 9 when divided by ten, etc. In fact, for any positive integer would give the remainders that you are looking for. I could prove this by induction, but I don't think you need that much.