Question

What is the remainder when (111...) + (222...) + (333...) + … + (777...) is divided by 37? In each bracket, the single digit (1, 2, 3, ..., 7) is written 110 times next to itself

Answer 1

You can calculate this directly.. Are you looking for a more clever trick? I'm looking but haven't found one yet..

Answer 2

I think it is 28 but not sure about the result, contribute to my logic, please
11111....= 1(11111....)
22222...,.= 2(11111...)
3333......=3(11111....)
4444.......=4(1111.....)
5555.......=5(11111....)
6666.......=6(1111......)
7777.......=7(111111...)
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=(1+2+3+4+5+6+7)(1111......)= 28(11111....)
now, calculate the (11111....) , 37|111= 3 so, 111 divided by 37 and remainder is 0
(11111......) 110 times of 1 that means we have 111 number of 1 and it is