Need some help understanding this
How many positive integers less than or equal to 123456 have a multiple that consists of all the same digits? (eg 101 works since 101 * 11 = 1111 which consists of only 1s)
Posted Nov 5, 2020, 9:25 PM UTC
11
How many positive integers less than or equal to 123456 have a multiple that consists of all the same digits? (eg 101 works since 101 * 11 = 1111 which consists of only 1s)
Posted Nov 5, 2020, 9:25 PM UTC
I’ll admit this method is absolutely awful but rather than spending ages trying to figure out a clever number theory answer you could just look at the factors of our unique digit numbers? Of course this is a cheap way to approach the question and I’m sure somebody else will have a better solution but still
I’d start by writing down all numbers that have a unique digit:
1,2,3,4,5,6,7,8,9
11,22,33,44,55,66,77,88,99
...
11111,22222,33333,44444,55555,66666,77777,88888,99999, 111111
You’ll have a total of 46 numbers; then just look at the factors of each of them and construct a list. Takes a while but then again so does any number theory question. Of course don’t look at the factors by hand; use this website! Your list will be pretty huge