What are the last 2 digits of the sum 1 + 11 + 111 + ... + 111...111 (last one has 50 digits)?

This is a question from Junior Math Olympiad.

Question : What are the last 2 digits of the sum 1 + 11 + 111 + ... + 111...111 (last one has 50 digits)?

Solution: Here is tiny python program. Also available http://www.codeskulptor.org/#user43_XiVvNuzfshT3lKX.py

# What are the last 2 digits of the sum 
# 1 + 11 + 111 + ... + 111...111 (last one has 50 digits?
total_num = 50
this_num = 0
sum = 0


for i in range(total_num):
            this_num = 10 ** i + this_num
            print "Number " + str(i+1) +":", this_num
            sum = sum + this_num

print "Total Sum:", sum



Output:

Number 1: 1
Number 2: 11
Number 3: 111
Number 4: 1111
Number 5: 11111
Number 6: 111111
Number 7: 1111111
Number 8: 11111111
Number 9: 111111111
Number 10: 1111111111
Number 11: 11111111111
Number 12: 111111111111
Number 13: 1111111111111
Number 14: 11111111111111
Number 15: 111111111111111
Number 16: 1111111111111111
Number 17: 11111111111111111
Number 18: 111111111111111111
Number 19: 1111111111111111111
Number 20: 11111111111111111111
Number 21: 111111111111111111111
Number 22: 1111111111111111111111
Number 23: 11111111111111111111111
Number 24: 111111111111111111111111
Number 25: 1111111111111111111111111
Number 26: 11111111111111111111111111
Number 27: 111111111111111111111111111
Number 28: 1111111111111111111111111111
Number 29: 11111111111111111111111111111
Number 30: 111111111111111111111111111111
Number 31: 1111111111111111111111111111111
Number 32: 11111111111111111111111111111111
Number 33: 111111111111111111111111111111111
Number 34: 1111111111111111111111111111111111
Number 35: 11111111111111111111111111111111111
Number 36: 111111111111111111111111111111111111
Number 37: 1111111111111111111111111111111111111
Number 38: 11111111111111111111111111111111111111
Number 39: 111111111111111111111111111111111111111
Number 40: 1111111111111111111111111111111111111111
Number 41: 11111111111111111111111111111111111111111
Number 42: 111111111111111111111111111111111111111111
Number 43: 1111111111111111111111111111111111111111111
Number 44: 11111111111111111111111111111111111111111111
Number 45: 111111111111111111111111111111111111111111111
Number 46: 1111111111111111111111111111111111111111111111
Number 47: 11111111111111111111111111111111111111111111111
Number 48: 111111111111111111111111111111111111111111111111
Number 49: 1111111111111111111111111111111111111111111111111
Number 50: 11111111111111111111111111111111111111111111111111
Total Sum: 12345679012345679012345679012345679012345679012340


Answer
Last 2 digit will be - 40



       

Comments

  1. You have a good point here!I totally agree with what you have said!!Thanks for sharing your views...hope more people will read this article!!! 333 angel number

    ReplyDelete

Post a Comment

Popular posts from this blog

Maximum number of 3-digit numbers that can be selected such that the sum of any two numbers is NOT divisible by 5

yamunaexpresswayauthority YEIDA refund