1. The problem asks which different numbers from 1 to 9 can be multiplied together to produce the same product. 2. We want to find pairs or sets of numbers $a, b, c, \ldots$ where each number is between 1 and 9, and $a \times b \times c \times \ldots = N$ for some product $N$, and there exist at least two different sets producing the same $N$. 3. Important rules: - Multiplication is commutative, so order does not matter (e.g., $2 \times 3 = 3 \times 2$). - We consider only distinct sets of numbers, ignoring order. 4. Let's check some examples: - $2 \times 6 = 12$ and $3 \times 4 = 12$; so 12 can be made by different pairs. - $1 \times 8 = 8$ and $2 \times 4 = 8$; so 8 can be made by different pairs. - $2 \times 2 \times 3 = 12$ and $3 \times 4 = 12$; so 12 can also be made by different sized sets. 5. Another example: - $1 \times 9 = 9$ and $3 \times 3 = 9$; so 9 can be made by different pairs. 6. Summary: Numbers like 8, 9, 12, and others can be formed by multiplying different numbers from 1 to 9. 7. To find all such numbers, one would list all products of combinations of numbers 1 to 9 and identify duplicates. Final answer: Numbers such as 8, 9, 12, and others can be formed by multiplying different numbers from 1 to 9.