N is a 5-digit positive integer, such that:

(i) N contains at least one 3 or at least one 7, and:
(ii) N is divisible by 37.

Determine the total number of values of N satisfying the given conditions.

My approximation:

There are 9*10^4  five digit numbers with no leading zero.

There are 7*8^4  five digit numbers with no leading zero,  containing neither 3 nor 7.

So there are 90000-28672 =61328 numbers satisfying condition 1.

Roughly 1/37 of these numbers i.e 1657 are divisible by 37. 

I am happy with this number as an engineer's approximation.

When some solver evaluates the exact number we will comment

upon the accuracy of my approximation. 

Posted by Ady TZIDON on 2015-08-06 13:18:46