I am a three digit number. My hundreds digit is the square of my ones digit. My tens digit is the product of my hundreds digit and my ones digit. What number(s) could I be?
so the tens digit is the ones digit cubed
any number greater than 2 has a two digit cube
000, 111, 482
To find the numbers that satisfy the given conditions, let's go step-by-step.
First, we know that the hundreds digit is the square of the ones digit. Since the ones digit can only be 0 to 9, the possible values for the hundreds digit are 0^2, 1^2, 2^2, ..., 9^2. This gives us the potential hundreds digits: 0, 1, 4, 9, 16, 25, 36, 49, 64, and 81.
Next, we know that the tens digit is the product of the hundreds digit and the ones digit. Taking the potential values we found earlier, we multiply each of them by their corresponding ones digits:
0 * 0 = 0
1 * 1 = 1
4 * 2 = 8
9 * 3 = 27
16 * 4 = 64
25 * 5 = 125 (not a valid tens digit since it is more than 9)
36 * 6 = 216 (not a valid tens digit for the same reason)
49 * 7 = 343 (not a valid tens digit for the same reason)
64 * 8 = 512 (not a valid tens digit for the same reason)
81 * 9 = 729 (not a valid tens digit for the same reason)
Since the tens digit must be between 0 and 9, the only valid tens digits from the list above are: 0, 1, and 8.
Finally, we combine the potential hundreds digits with the valid tens digits to find the possible three-digit numbers:
Numbers with hundreds digit 0: 0 * 0 * 0 = 0
Numbers with hundreds digit 1: 1 * 1 * 1 = 1
Numbers with hundreds digit 4: 4 * 4 * 4 = 64
Numbers with hundreds digit 9: 9 * 9 * 9 = 729
Therefore, the possible three-digit numbers that satisfy the given conditions are: 0, 1, 64, and 729.