There is such a three-digit number, the number in the tens place is three times the number in the hundreds place, the number in the ones place is larger than the number in the hundreds place and smaller than the number in the tens place, and the number in the hundreds place The three-digit number obtained by exchanging places with the ones digit is 297 larger than the original three-digit number. How many such three-digit numbers are there?
有这样的三位数，它的十位上的数是百位上的数的3倍，个位上的数比百位上的数大比十位上的数小，把百位上的数与个位上的数交换位置得到的三位数比原三位数大297．这样的三位数一共有多少个．
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