Puzzles
8 December
What is the largest number of factors which a number less than a million has?
Fill in the digits
Source: Chalkdust
![](javascript:showlimage("chalkdust-puzzle.png"))
Can you place the digits 1 to 9 in the boxes so that the three digit numbers formed in the top, middle and bottom rows are multiples of 17, 25 and 9 (respectively); and the three digit numbers in the left, middle and right columns are multiples of 11, 16 and 12 (respectively)?
N
Consider three-digit integers \(N\) such that:
(a) \(N\) is not exactly divisible by 2, 3 or 5.
(b) No digit of \(N\) is exactly divisible by 2, 3 or 5.
How many such integers \(N\) are there?