1. The problem is to arrange the digits 1, 2, 3, 5, 6, 7 in the gaps of the equation $$\square . \square \square \times 2 = \square \square . \square$$ so that the multiplication is correct. 2. Let the number on the left side be $a.bc$ where $a$, $b$, and $c$ are digits from the given cards. 3. The right side is $de.f$ where $d$, $e$, and $f$ are digits from the cards. 4. The equation is: $$ (a + \frac{b}{10} + \frac{c}{100}) \times 2 = d + \frac{e}{10} + \frac{f}{100} $$ 5. Multiply the left side by 2: $$ 2a + \frac{2b}{10} + \frac{2c}{100} = d + \frac{e}{10} + \frac{f}{100} $$ 6. Since the right side is a decimal with two digits before the decimal point and one digit after, $d$ and $e$ form a two-digit number, and $f$ is the decimal digit. 7. We try to find digits $a,b,c,d,e,f$ from {1,2,3,5,6,7} without repetition that satisfy the equation. 8. Test possible values for $a$ (1 to 7) and calculate $2 \times (a.bc)$ to see if it matches the form $de.f$ with digits from the set. 9. Try $a=3$, $b=5$, $c=6$: $$3.56 \times 2 = 7.12$$ Check digits: 3,5,6,7,1,2. But 1 and 2 are in the set, so this works. 10. Verify digits are from the set {1,2,3,5,6,7} and no repetition: Left: 3,5,6 Right: 7,1,2 All digits used once. 11. Therefore, the correct arrangement is: $$3.56 \times 2 = 7.12$$