思维链

If John has 3 apples and gives half to Mary, then buys 4 more, how many does he have?

Let's think step by step.

Example 1:
Q: A baker has 24 cupcakes. She puts them equally into 4 boxes. Then she eats 2 cupcakes from one box. How many cupcakes total remain?

A: Let's work through this:
- Total cupcakes: 24
- Cupcakes per box: 24 ÷ 4 = 6
- After eating 2 from one box: 6 - 2 = 4 cupcakes in that box
- Total remaining: (3 boxes × 6) + 4 = 18 + 4 = 22 cupcakes

Example 2:
Q: A train travels at 60 mph for 2 hours, then 40 mph for 3 hours. What is its average speed?

A: Let's work through this:
- Distance at 60 mph: 60 × 2 = 120 miles
- Distance at 40 mph: 40 × 3 = 120 miles
- Total distance: 120 + 120 = 240 miles
- Total time: 2 + 3 = 5 hours
- Average speed: 240 ÷ 5 = 48 mph

Now solve:
Q: A store sells notebooks for $3 each. If you buy 10 or more, you get 25% off. How much do 12 notebooks cost?

Use this template to solve the problem:

GIVEN: [List known information]
GOAL: [What we need to find]
APPROACH: [Strategy we'll use]
STEPS:
1. [First step with reasoning]
2. [Second step with reasoning]
...
VERIFICATION: [Check the answer]
ANSWER: [Final answer]

Problem: A car uses 8 liters of fuel per 100 km. If the tank holds 45 liters and fuel costs $1.50 per liter, how much does it cost to drive 300 km?

A company's revenue was $1.2M in Q1. It grew 15% in Q2, declined 10% in Q3, and grew 25% in Q4. What was the total annual revenue?

Think through each quarter, showing your calculations clearly.

Three friends—Alice, Bob, and Carol—each have different pets (cat, dog, fish) and different jobs (teacher, engineer, doctor).

Clues:
1. Alice doesn't have a cat
2. The engineer has a dog
3. Bob is a teacher
4. Carol doesn't have a fish

Who has which pet and job? Reason through this systematically, testing hypotheses and verifying against all clues.

This function should return the sum of even numbers in a list, but it's returning wrong values. Debug step by step by tracing through with the input [2, 3, 4, 6]:

def sum_evens(numbers):
  total = 0
  for n in numbers:
      if n % 2 == 0:
          total += 1
  return total

Trace each step, find the bug, and provide the fix.

Solve this problem 3 different ways, then give your final answer based on which solution appears most correct:

Problem: A farmer has chickens and cows. Together they have 30 heads and 74 legs. How many chickens and how many cows does the farmer have?

Approach 1: Algebra
Approach 2: Guess and check
Approach 3: Logical reasoning

Then compare and give your final answer.

Should we adopt microservices architecture for our application?

Context:
- Monolithic application with 50,000 lines of code
- Team of 5 developers
- 100 daily active users
- Planning for 10x growth in 2 years

Think through this systematically:
1. List the current state
2. Identify factors to consider (team size, scale, velocity, future growth)
3. Weigh each factor as for/against
4. Give a recommendation with reasoning