dawoodr Posted September 16, 2014 Share Posted September 16, 2014 (edited) Along a road, there exists marks for every passed kilometer after every kilometer, at the start where the mark shows 0. A hiker who starts walking at the roads start devote himself to count the numbers on the marks. How many kilometers has the hiker walked/passed at the mark showing the number 2013?I have the solutions aswell but I don't understand the solution. You can see it below. Solution: The single digit numbers add up to 10 numbers and corresponds to 9 passed kilometers. The two digit numbers together holds a total of 180 numbers(I don't get this part). When you pass the sign with the number 99, which is the biggest two digit number, you have walked a total of 9+90=99km. All the three digit numbers together contain 3 · 900 > 2013 numbers. So, when one have passed the sign with the 2013 number/digit one have walked atleast a three digit number of kilometers. We have the following: 2013 = 10 + 180 + 6 · (3 · 100) + 3 · 7 + 2; which means that at the sign with the 2013th digit, one passed 9 + 90 + 6 · 100 + 7 + 1 = 707 kilometers. If somebody could explain this I would be greatful. Regards! Edited September 16, 2014 by dawoodr Link to comment Share on other sites More sharing options...
imatfaal Posted September 16, 2014 Share Posted September 16, 2014 Seems a very silly problem - I think you are counting the cumulative number of printed characters on the kilometre posts. single digits 0-9 inclusive - 10 kilometre posts - 10 characters - 9 kilometres (0-9) double digit 10-99 incl - 90 kilometre posts - 180 characters - 90 kilometres (9-99) triple digits 100-999 - 900 km posts - 2700 characters - 900 km (99-999) so as the solution says you will pass the 2013 character during the three digits km posts I would do it this way: total number of characters passed at 99 km is 190. 2013-190 = 1823. So you have 1823 characters in the three character range. 1823 / 3 = 607.66. So you have to pass the 608th km post so 9 km for single character km posts 90 km for double character km posts 608 km for a portion of the triple character km posts 9+90+608=707km 1 Link to comment Share on other sites More sharing options...
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