Counting A Huge Number
What's the 500th digit of the number
1223344455567788999101010
11121213131414141515151617171818191919202020 …… 101102102103103104104104105105105……
Hint：it follows a pattern (a bb cc ddd eee, f gg hh iii jjj…… )
The answer is 1.
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1 solution
If we divide this huge number into groups as mentioned(a bb cc ddd eee),
we can see :
1-10 occupy 25 digits (11*1+14),11 digits per group,1 regular group and a group taking 101010 into account(11+3)
11-100 occupy 399 digits (22*17+25),22 digits per group ,17 regular groups (20-2(used)-1) and a group taking 100100100 into account (22+3)
We have 500 digits in total,424 digits have been used , therefore 76 digits are left.
then we count from 101,following the pattern ,there are 33 digits per group
because 33*2=66 ,another 2 regular groups are used,
76-66=10 ,10 digits left
then we count from 111,10=3*3+1
therefore the 500th digit should be 1.