Problema Solution
A policeman investigates a robbery in a street nearby.Their only clue was this message from the suspect:
There is a 9-digit number containing the numbers 1 through 9.Each number is only used once.This 9-digit number is divisible by 9.When you take off the right-most digit,it becomes an 8-digit number that is divisible by 8!When you take off the last digit to create a 7-digit number,the whole number is now divisible by 7.The pattern continues all the way down until the end,when it is a two digit number divisible by two,and then taking off the end digit creates a 1-digit number,divisible by 1.
Answer provided by our tutors
The 5th digit can only be 5 since any number ending in 5 is only divisible by 5 if 0 is not permitted.
The sum of 4th, 5th and 6th must be divisible by 3, so these digits can be 258 or 654 (in this order, since 3rd digit is odd and the divisibility rule by 4 yields 4th digit 2 or 6). First option leads to last digits 963, but the divisibility by 7 test fails and should be rejected. The second option yields the 8th digit 8 or 2, but the 7th, being odd excludes 8, so the last 3 digits can be 723 or 729. Next test (divisibility by 7) leads to the answer.
The answer is 381654729.