In the diagram below, each circle represents a digit. Fill in the diagram by placing one of the digits from 0 to 9 in each circle, using each digit only once.

$$
\text { ○×○○×○○○=○○○○ }
$$

## Solutions to List 6
Let $a, b, c, \ldots$ be the numbers in each circle as indicated below.

## $(a) \times(b)(c) \times(d)(e) f=(g)(b)(j)$

We know that $a, c$ and $f$ cannot be zero, because $0 \times x=0$.

However, the product of the three numbers is a four-digit number, so $a b d<10$ and therefore the numbers that appear in the said product are $1,2,3$ or $1,2,4$. Observe that the second is impossible because the minimum product we can obtain in this case is

$$
1 \times 23 \times 456=10488
$$

Thus, $a b d=6$ and the product is greater than 6000. On the other hand, $a$ cannot be 2 or 3 because in that case the minimum value of the product is

$$
2 \times 14 \times 356=9968
$$

and the other products are greater than 10000. Therefore, $a=1$.

Continuing this analysis, we obtain the solution:

$$
(1) \times(2) \times(3)(4)=8(9)(7)(0)
$$