Today's Puzzle No.11 Find the number.?

Wednesday, December 22, 2010

Question:

A number of 9 digits has the following properties:

• The number comprising the leftmost two digits is divisible by 2, that

comprising the leftmost three digits is divisible by 3, the leftmost four by 4,

the leftmost five by 5, and so on for the nine digits of the number i.e. the

number formed from the first n digits is divisible by n, 2<=n<=9.

• Each digit in the number is different i.e. no digits are repeated.

• The digit 0 does not occur in the number i.e. it is comprised only of the

digits 1-9 in some order.

Find the number.

Answer:

The answer is 381654729

One way to solve it is Trial-&-Error. You can make it bit easier as odd positions
will always occupy ODD numbers and even positions will always occupy EVEN
numbers. Further 5th position will contain 5 as 0 does not occur.
The other way to solve this problem is by writing a computer program that
systematically tries all possibilities