Formula for Sequential Sub-Problem Solving

Example of a Complex Number Arithmetic Problem

A system is tasked with solving the following logic puzzle: 'A bakery started with 15 donuts. They sold one-third of them in the morning and then baked 6 more. How many donuts do they have now?' The system considers two distinct methods to find the answer.

Method A:

1. Generate a list of plausible final answers: {12, 14, 16, 18}.
2. For each plausible answer, check if it can be reached from the starting conditions. For '16', the check is: (15 - 15/3) + 6 = (15 - 5) + 6 = 10 + 6 = 16. This is consistent.
3. Select 16 as the final answer.

Method B:

1. Calculate the number of donuts sold: 15 / 3 = 5.
2. Calculate the number of donuts remaining after sales: 15 - 5 = 10.
3. Calculate the new total after baking more: 10 + 6 = 16.
4. State 16 as the final answer.

Which of these methods best illustrates the concept of forming a logical chain of intermediate steps that progresses from the initial problem to the final solution?

A system is tasked with solving the following problem: 'A company's profit was $50,000 in the first quarter. In the second quarter, it increased by 20%. In the third quarter, it decreased by $10,000 from the second quarter's profit. What was the profit in the third quarter?' Arrange the following actions into a logical, step-by-step reasoning path to arrive at the correct solution.

Constructing a Reasoning Path for a Word Problem

Formal Representation of a Solution as a Sequence of Reasoning Steps