Here's how we can formulate this problem and the corresponding Gurobi code:

**Decision Variables:**

* `x`: Number of easy puzzles solved
* `y`: Number of hard puzzles solved

**Objective Function:**

Maximize points: `5x + 8y`

**Constraints:**

* At least 3 easy puzzles: `x >= 3`
* At least 1 hard puzzle: `y >= 1`
* At most 10 easy puzzles: `x <= 10`
* At most 5 hard puzzles: `y <= 5`
* Total puzzles at most 10: `x + y <= 10`

```python
import gurobipy as gp

# Create a new model
m = gp.Model("puzzle_optimization")

# Create variables
x = m.addVar(vtype=gp.GRB.INTEGER, name="x") # easy puzzles
y = m.addVar(vtype=gp.GRB.INTEGER, name="y") # hard puzzles

# Set objective function
m.setObjective(5*x + 8*y, gp.GRB.MAXIMIZE)

# Add constraints
m.addConstr(x >= 3, "easy_min")
m.addConstr(y >= 1, "hard_min")
m.addConstr(x <= 10, "easy_max")
m.addConstr(y <= 5, "hard_max")
m.addConstr(x + y <= 10, "total_max")

# Optimize model
m.optimize()

# Print results
if m.status == gp.GRB.OPTIMAL:
    print(f"Optimal solution found: Solve {x.x} easy puzzles and {y.x} hard puzzles")
    print(f"Total points: {m.objVal}")
elif m.status == gp.GRB.INFEASIBLE:
    print("Model is infeasible")
else:
    print(f"Optimization ended with status {m.status}")

```
