Talk:2019 AMC 10B Problems/Problem 19

I think there's a generalisation for this? I've noticed that for 10, we have 5 possibilities, or 6-1 (6 possibilities, subtract 1 repeated number) For 100, I brute forced it and got 28-15 (28 possibilities, subtract 15 repeated numbers) For 1000, I did a pro gamer move and brute forced it so hard my pen ran out of ink and got 105-36 (105 possibilities, subtract 36 repeated numbers) And now for 100000, we have the answer as 117, or 253-136 Noticed anything? The numbers we have are all triangle numbers! if T(n) = the nth triangle number and S(n) is the possibilities for 10^n, then we have T(3)-T(1)=S(1) T(7)-T(5)=S(2) T(15)-T(9)=S(3) I don't have S(4), since I wasn't brave enough to brute force it, but I'll write something here later I hope and now T(23)-T(16)=S(5) is this some pattern or something? -hotmonkey1