How many 3 digit numbers are there, in which when put in reverse order, create a larger number?

How many 3 digit numbers are there, in which when put in reverse order, create a larger number?





like, 257==%26gt;752How many 3 digit numbers are there, in which when put in reverse order, create a larger number?
there are 324 numbers... why?


100-200 = all numbers endind with 2-9 will be bigger if you reversed... there are 8 numbers from 100-110, 8 numbers from 111-120..so on... there are 72


201-300- all numbers ending in 3-9... there are 63


301-400- all numbers ending in 4-9..54


401-500- all numbers ending in 5-9...45


501-600-all numbers ending in 6-9...36


601-700- all ending in 7-9...27


701-800-all ending in 8-9...18


801-900-all ending in 9...9


900-999= no more because if you reversed them, it will be smaller..


add all and you will get 324...you can try all the numbers listed above...How many 3 digit numbers are there, in which when put in reverse order, create a larger number?
Alright to solve this problem you have to know that the number:





abc is smaller than cba, where the letters are digits





This means that c has to be larger than a, while b doesn't matter (for now).





So since a can be anywhere between 1 and 9 (inclusive), you will just have to brute force it:





IF...


a = 1


c=2,3,4,5,6,7,8,9





a=2


c=3,4,5,6,7,8,9


.


.


.





Now once you have all of the possiblilities (36) this is where digit b comes in. Since there are 10 number b can be (0 - 9) you will have to multiply the possibilities by 10 to get the total amount. (360)





The reason why you can't use the usual combination trick is because while there are 8 possible for the first digit and 9 for the last, not all of those 72 (a,c) pairs agree with the restriction: a%26lt;c.
in the first digit you have 8 choices 1,2,3,4,5,6,7,8, assuming you cant say 023, then middle digit is 10 choices 0,1,2,3,4,5,6,7,8,9 and finally last digit can be 2,3,4,5,6,7,8,9 or 8 choices so 8*8*10=640 choices.
Prolly about 500, there are 1000 three digit numbers, (not counting decimals) and lets assume that there is a 50% chance that they reverse to be larger, so that gives me 500.......
give up