We call a number a mountain number if its middle digit is larger than any other digit. For example, 284 is a mountain number. How many 3-digit mountain numbers are there?
With 2 in the middle, you have = 2 numbers[1 x 2] - 120, 121
With 3 in the middle, you have = 6 numbers[2 x 3] - 130, 131, 132, 230, 231, 232.......and so on.
With 4 in the middle, you have = 12 numbers[3 x4]
With 5 in the middle, you have = 20 numbers[4 x 5]
With 6 in the middle, you have = 30 numbers[5 x 6]
With 7 in the middle, you have = 42 numbers[6 x 7]
With 8 in the middle, you have = 56 numbers[7 x 8]
With 9 in the middle, you have = 72 numbers[8 x 9]
So, you have a total of =2 + 6 + 12 + 20 + 30 + 42 + 56 + 72 = 240 "monutain numbers"
Note: Make sure you check them to see if I skipped any.
