How many 3-digit numbers can be written as the sum of three (not necessarily different) 2-digit numbers?
ALL the 2-digit numbers from 34 -99 = 66 numbers, when added 3 at a time, will make a 3-digit number. So, theoretically, you could have as many as 66 C 3 =45,760 3-digit numbers!!! In addition, if you are allowed to, you can take any of the 66 numbers and multiply it by 3, which is the same as adding them 3 times such as: 34 + 34 + 34 =102. However, since there are only 900 3-digit numbers between 100 and 999, most of the above numbers will be duplicates many times over.