I'm thinking of a ten-digit integer whose digits are all distinct. it happens that the number formed by the first n of them is divisible by n for each n from 1 to 10. what is my number?

The problem here takes a brilliant mind to answer this. This problem can easily be answered using programming because we can not then and there push all the possibilities using paper and pen.

The answer is 3816547290. 

Trying all the possibilities starting form 1000000080 (we are sure that the last number should be 0). Then traversing that number until 9999999990. Each traverse, check the number if its divisible to n, so on and so forth.

the law of definite proportions states samples of a compound will always contain the same proportion of elements by mass. in other words, a given compound will always contain the same elements in the same proportions by mass.the law of multiple proportions states when two elements combine with each other to form more than one compound, then the weights of one element that combine with a fixed weight of the other are in a ratio of small whole numbers.