Math Is Fun Forum

Melllyy

Guest

Numbers

If all the intergers from 1 to 1000 (including 1 and 1000) were written down, how many times would the digit 1 be written.

For example 121 the digit 1 is written twice

mathsyperson

Moderator

Registered: 2005-06-22

Posts: 4,900

Re: Numbers

Consider each column (units, tens and hundreds) separately.
From 0 to 9, 1 is written once. Looking at the units only, this is also true for 10-19, for 29-29 and so on.

There are 100 groups of ten numbers, all of which have a single "unit 1". So there are 100 "unit 1's" in all.

Similar arguments can be made for the ten and hundreds columns, meaning that when you write 1-999, you write 300 ones.

Add an extra one for the thousand, and you get a final answer of 301.

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Why did the vector cross the road?
It wanted to be normal.

neodama

Guest

Re: Numbers

Hi,

U still haven't answered Melllyy's question: your method only counts the unit 1. She's ALSO after the tens & hundreds.

JaneFairfax

Member

Registered: 2007-02-23

Posts: 6,868

Re: Numbers

Mathsyperson’s solution is correct!