N is a duodecimal (base 12) positive integer having precisely 50 digits such that each of its digits is equal to 1 except the 26th digit. If N is divisible by the duodecimal number 17, then find the digit in the 26th place.
If the digits were all 1's, the value of the number, in decimal would be (12^50  1)/11. When taken mod 19 decimal that comes out as 13 decimal.
The 25th position has place value 12^24, which, mod 19, is 1
So we need to add another 1913 = 6 to that position, making it a 7.
The calculations were done in immediate UBASIC:
?(((12^50)1)//11)@19
13
OK
?(12^24)@19
1

Posted by Charlie
on 20100529 15:57:08 