Find an 8-digits number such that ....

(June 29th, co-located with STOC, will be a workshop to celebrate  Vijay Vazarani's 60th birthday. As computer scientists shouldn't we use 64 as the milestone? See here for details about the workshop, not about 60 vs 64.) I will likely post a lot about Gathering For Gardner 13, but for now I will just give one problem I saw there. I will not say the speaker or the title of the talk as that might be a clue. I'll give the answer in my next post which will be this week Find an 8-digit number d_7 d_6 d_5 d_4 d_3 d_2 d_1 d_0 such that d_0 is the number of 0's in the number d_1 is the number of 1's in the number d_2 is the number of 2's in the number ..... d_6 is the number of 6's in the number but d_7 is NOT necc the number of 7's d_7 is the number of DISTINCT DIGITS in d_7 d_6 d_5 d_4 d_3 d_2 d_1 d_0 You could prob find such a number by computer search- but don't. Feel free to comment. I will not block comments (except those we usually block- usually spam)  but by the same token, if you don't want hints, don't read the comments.