10. Among three-digit numbers, if the digit in the tens place is smaller than the digits in the hundreds and units places, the number is called a concave number, such as 504, 746, etc., which are all concave numbers. Therefore, among three-digit numbers with no repeated digits, the number of concave numbers is $\qquad$.
10. 240 .

When the tens digit is 0, there are $9 \times 8$ concave numbers that meet the condition, when the tens digit is 1, there are $8 \times 7$ concave numbers that meet the condition, .....
When the tens digit is 7, there are $2 \times 1$ concave numbers that meet the condition, in total there are $72+56+42+30+20+12+6+2=240$.
