A number of 50 digits has all its digits equal to 1 except the 26th digit. If the number is divisible by 13, then find the digit in the 26th place.

(In reply to solution by Charlie)

The mod-13 values could be found directly via extended precision provided by UBASIC:

list


   10   point 15


   20   for I=0 to 49


   30     N=N+10^I


   40   next


   50   print N@13


   60   print (10^24)@13


OK


run


 11


 1


OK





telling us the original mod value and the mod value


for each additional point in the 26th position, then:





? 11111111111111111111111113111111111111111111111111 @ 13


 0


OK

---------
With the latter immediate-mode print command (the ?) being a check on the answer.

Posted by Charlie on 2003-11-15 11:46:40