Go Computer... :D

Number Theory Level 3

A Computer is Programmed to scan digits of the counting numbers. For Example, if it scans: 123456789101112, then, it has scanned 15 digits. The Computer Begins it's task and scans the first 1788 digits. Find the last counting number scanned.


The answer is 632.

View wiki
Christian Daang by Christian Daang , 20, Philippines

This section requires Javascript.
You are seeing this because something didn't load right. We suggest you, (a) try refreshing the page, (b) enabling javascript if it is disabled on your browser and, finally, (c) loading the non-javascript version of this page . We're sorry about the hassle.

2 solutions

Christian Daang
Oct 24, 2014

The digits,

1-9 = 9 digits,

10 - 99 = 2(90) = 180 digits

1-99 = 189 digits

Then,

1788 - 189 = 1599

then,

100-999 = 3(900) = 2700 digits

Then, the formula is...

3(n-99) = 1599, where in, n is the last counting number:

3n - 297 = 1599

3n = 1896

n = 632

Final Answer: 632...

1 Helpful 0 Interesting 0 Brilliant 0 Confused

Nice. s/Begins it's/begins its/

a s - 6 years, 7 months ago
Shohag Hossen
Dec 10, 2014

Sample counting number is = 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 13, 14, 15,-----100 , 101 ,------, 632 . Now, add every digit of this counting number. This is answer.

1 to 9 = 9 * 1 (digit)= 9.

10 to 99 = 90 * 2 (digit)= 180. ( Here 90 is come from , 99 -10 + 1 =90 )

100 to 632 = 533 * 3 (digit)= 1599.

( Here 533 is come from , 632 -99 + 1 =533 )

Now, 9 + 180 + 1599 = 1788.

So, last counting number is = 632.

answer = 632

0 Helpful 0 Interesting 0 Brilliant 0 Confused

0 pending reports

×

Problem Loading...

Note Loading...

Set Loading...