Hostile Divisor Numbers (Easy version)
Some divisors of positive integers really hate each other and they don't like to share one or more common digits.
For example the number
886
has 4 divisors:
1, 2, 443 and 886
(as you can see,
no two of them share the same digit
).
Thus,
886
is a
H
ostile
D
ivisor
N
umber (
HDN
) but
889 is NOT
because its divisors (1, 7, 127, 889) share some common digits.
(7 and 127 have both 7 as a digit)
There are
26 HDN
under
100
:
1, 2, 3, 4, 5, 6, 7, 8, 9, 23, 27, 29, 37, 43, 47, 49, 53, 59, 67, 73, 79, 83, 86, 87, 89, 97
How many HDN are there under 1000 ?
Can you also solve the Hard version ?
The answer is 119.
This section requires Javascript.
You are seeing this because something didn't load right. We suggest you, (a) try
refreshing the page, (b) enabling javascript if it is disabled on your browser and,
finally, (c)
loading the
non-javascript version of this page
. We're sorry about the hassle.
1 solution
There are 119 HDN under 1000:
1,2,3,4,5,6,7,8,9,23,27,29,37,43,47,49,53,59,67,73,79,83,86,87,89,97,223,227,229,233,239,257,263,267,269,277,283,293,307,337,347,349,353,359,367,373,379,383,389,397,409,433,439,443,449,457,463,467,479,487,499,503,509,523,547,557,563,569,577,587,593,599,607,623,643,647,653,659,673,677,683,687,706,709,727,733,739,743,757,766,769,773,787,797,807,809,823,827,829,839,853,857,859,863,866,877,878,883,886,887,907,929,937,947,953,967,977,983,997I found them using Mathematica and here is the plot