problem: Find the number of 2's from 100 to 400?

[donnalatrell]

What is the formula for finding out the number of 2's from 100 to 400? I know the answer but cannot figure out how to compute.

 

[Loren]

Someone probably has a formula for that. I don't. So I would just add them up. How many 2's would be in the hundreds position? I'm thinking there are 100---all the 200's---from 200 through 299. Next how many 2's are in the tens position? Then, how many twos in the units position? A little analysis and a little addition and you have your answer.

 

[jwpaine]

Re: Math Problem

What is the formula for finding out the number of 2's from 100 to 400? I know the answer but cannot figure out how to compute.

\(\displaystyle \L \frac{400-100}{2}\) ?

 

[Denis]

20 for each 100 range, plus 100 for the 200 range
r = 100 ranges
earth shaking formula: 20r + 100

We have 3 ranges (100-199, 200-299, 300-399), so 20*3 + 100 = 160

 

[donnalatrell]

Thanks to all who answered my post regarding how many 2's are in the numbers 100 to 400. I tried 2 of the answers and all three were wrong. The answer is 138?? Still do not know how to come up with this so if any of you have any more ideas please let me know. Thanks so much, Donna

 

[Denis]

Donna, the answer is 160: whoever tells you that's wrong is WRONG :wink:

There is 20 in any 100 range; take 100-199:
102, 112, 120, 121, 122 (this one has two), 123, 124, 125, 126, 127, 128, 129,
132, 142, 152, 162, 172, 182, 192 : that's 20, right?

So that's 60 for 3 ranges.

But range 200-299 contains another 100: the 1st digit of each.
Get my drift?

If you're still not convinced, write doen ALL the numbers from
100 to 400, then count the 2's !

 

[daon]

If you don't count repititons you'd have 100 for the 200's and 19 for the 100's and 300's = 100+19+19=138.

The correct question to this answer should be "How many numbers between 100 and 400 have at least one two in them," not what has been stated.