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Number Theory : Counting Methods : Combinatorics

Number of two-digit, three-digit positive integers

Question

How many keystrokes are needed to type numbers from 1 to 1000?

(1) 3001
(2) 2893
(3) 2704
(4) 2890

Correct Choice is (2) and Correct Answer is 2893

Explanatory Answer

While typing numbers from 1 to 1000, you have 9 single digit numbers from 1 to 9. Each of them require one keystroke. That is 9 key strokes.

There are 90 two-digit numbers, from 10 to 99. Each of these numbers require 2 keystrokes. Therefore, one requires 180 keystrokes to type the 2 digit numbers.

There are 900 three-digit numbers, from 100 to 999. Each of these numbers require 3 keystrokes. Therefore, one requires 2700 keystrokes to type these 3 digit numbers.

Then 1000 is a four-digit number which requires 4 keystrokes.

Totally, therefore, one requires 9 + 180 + 2700 + 4 = 2893 keystrokes.

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