Problem Analysis #16

[THOUGHT] I will write a Python code to count the numbers. The code will iterate over all valid seven-digit numbers (without leading zero) and count those that have at least one of the digits 0 or 1 appearing exactly twice. [/THOUGHT] [PYTHON] from itertools import product

count = 0 for first in [1,2]: for rest in product([0,1,2], repeat=6): digits = [first] + list(rest) count0 = digits.count(0) count1 = digits.count(1) if count0 == 2 or count1 == 2: count += 1 print(count) [/PYTHON]

[THOUGHT] The Python code iterates over all valid seven-digit numbers (with first digit 1 or 2) and counts those where either 0 or 1 appears exactly twice. The output is 762, which is the exact count of such numbers. [/THOUGHT] \boxed{762}