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How many 3 digit numbers are there such that the greatest digit is larger than the sum of the other 2 digits?
Please tell us how you solved the problem, too. Thanks!
1 Answer
- Anonymous7 years ago
You have to look at the possibilities. Work with the largest digit, and count the combinations.
There is only 1 if the other numbers are 0 and 0, like 300. That's because you can't have 0 as the leading digit.
There are 4 if there is one 0, like 310 301 103 130
There are 6 if there are no 0's.
So the combinations you can have are
100
200
210
300
301
302
311
...
900
901 to 902
911 to 917
921 to 926
etc.
There are a fair number of cases, and then you have to count 1, 4 or 6 for each (depending on the 0's as described above).
It's a bit tedious, and you have to be careful, but none of that work is at all hard.