Question

Counting Problem:

How many 3 digit positive numbers are there in which the tens and units digits are different?

Answer 1

ddddddd

Answer 2

We'll try to diagram this to better appreciate the calculation.

Answer 3

If we consider 000 a positive number (some folks may exclude 000 as a positive),
there are then 1000 possible combinations if we have no other exclusions/constraints.

Answer 4

This is because we can choose any digit from 0 to 9 for each placeholder.

Answer 5

Since there would be 10 choices for each placeholder with each placeholder independent of the others, the total would be 10 * 10 * 10 or 1000.

However,

Answer 6

so 3 digit postives means you start at

100...

001 isn't considered a 3 digit number

Answer 7

However, this particular problem is a bit more complicated.

Answer 8

so you have 9 choices for 1st

Answer 9

We have the constraint that the tens digit and ones digit must be different.

Answer 10

we need to decide if 001 is considered a 3 digit number here.
Or does this problem want us to consider 100 to 999?

Answer 11

Is 001 considered as a possible 3 digit number for this problem?
Or do we need to start at 100?

Answer 12

so for me its 9 x 10 x 9

Answer 13

that is correct ^ - provided we start with 100.

Answer 14

If we start counting with 100, there are 9 possible choices for the 1st digit.
We then have 10 possible choices for digit 2.
We then have 10 possible choices for digit 2, there are 9 choices for digit 3.

Answer 15

So teh total number of possibilities here is 810.

Answer 16

an alternate method

number of possible 3 digit number - number of3 digit number with last 2 the same

Answer 17

Can you see how the calculation would need to be modified if the 3rd digit needs to be the same as teh 2nd digit? @Chibi_Robo3

Answer 18

oh yeah, thanks!
i got it :)

sorry I was busy doing my the other questions.

Answer 19

No worries, my pleasure. :)