TITLE: What is the smallest positive multiple of 450 whose digits are all zeroes and ones?
QUESTION [50 upvotes]: What is the smallest positive multiple of 450 whose digits are all zeroes and ones?
I tried guess and check but the numbers grew big fast.  Thanks in advance!

REPLY [2 votes]: one more way. let x be the required number.
for a number to be multiple of 450, it should be multiple of 10.  so 10.y =x
now y should be multiple of 45. it should be first multiple of 5. so a number with only 1, o will be multiple of 5 if last digit is 0.
 so y = 2. w/9...dividing 10 by 5 gives 2 in numerator.
2.w should be mulitple of 9 and should contain only 1,0.
using the fact that sum of digits should be multiple of 9 for a number to be multiple of 9,
2.w should be 111111111.
adding two zeros extra.
11111111100.
thus 11111111100 is the required number.
lengthy process but easy to understand.