Final answer:
The question involves finding digits for a, b, and c to satisfy the equation ab*bc=cac, under the constraint that a, b, and c range from 1 to 9 and each forms a significant part of two- and three-digit numbers.
Step-by-step explanation:
The question is asking to solve a numerical puzzle where a, b, and c are digits from 1 to 9 and are used to form two-digit and three-digit numbers. The specific puzzle states that ab multiplied by bc equals cac, with ab and bc representing the two-digit numbers and cac the three-digit number with a repeated digit.
Since we are restricted to the digits from 1 to 9, we can infer that c cannot be 1 because that would make cac too small compared to the product of two two-digit numbers. The digit c should make cac large enough to reasonably be the product of ab and bc. This sort of reasoning involves understanding significant digits and making calculations to find numbers that abide by the rules of the puzzle. By exploring all possibilities with logical elimination, we should be able to find the correct digits for a, b, and c.