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+# Math Problem Solving - MCTS Example
+
+This example demonstrates using MCTS to solve a math problem by exploring different solution strategies.
+
+```julia
+using LLMMCTS
+
+# State represents the current state of problem solving
+# It contains the problem statement and the steps taken so far
+
+function math_problem_transition(state::Dict, args::NamedTuple)
+    current_step = get(state, :step, 0)
+    problem = state[:problem]
+    
+    # Example problem: Solve x^2 = 16
+    if current_step == 0
+        # First step: analyze the problem
+        newstate = Dict(
+            :step => 1,
+            :thought => "This is a quadratic equation x^2 = 16",
+            :action => "Take square root of both sides",
+            :reward => 2.0,
+            :isterminal => false
+        )
+        progressvalue = 5.0
+    elseif current_step == 1
+        # Second step: solve
+        newstate = Dict(
+            :step => 2,
+            :thought => "Taking square root gives x = ±4",
+            :action => "x = sqrt(16) or x = -sqrt(16)",
+            :reward => 3.0,
+            :isterminal => false
+        )
+        progressvalue = 7.0
+    elseif current_step == 2
+        # Third step: verify
+        newstate = Dict(
+            :step => 3,
+            :thought => "Verify both solutions work",
+            :action => "Check x=4: 4^2=16 ✓, Check x=-4: (-4)^2=16 ✓",
+            :reward => 5.0,
+            :isterminal => true  # Problem solved!
+        )
+        progressvalue = 10.0
+    else
+        # Terminal state
+        newstate = Dict(
+            :step => current_step,
+            :thought => "Problem solved",
+            :action => "Solution complete",
+            :reward => 10.0,
+            :isterminal => true
+        )
+        progressvalue = 10.0
+    end
+    
+    return Dict(
+        :newNodeKey => "step_$current_step",
+        :newstate => newstate,
+        :progressvalue => progressvalue
+    )
+end
+
+# Initial state
+initialstate = Dict(
+    :step => 0,
+    :problem => "Solve x^2 = 16",
+    :reward => 0,
+    :isterminal => false
+)
+
+# Transition arguments
+transitionargs = ()
+
+# Run MCTS
+result = runMCTS(
+    initialstate,
+    math_problem_transition,
+    transitionargs;
+    maxiterations = 15,
+    explorationweight = 1.0,
+    maxSimulationDepth = 3,
+    horizontalSampleExpansionPhase = 3
+)
+
+# Display results
+println("Problem: ", initialstate[:problem])
+println()
+println("Best solution trajectory:")
+println("  Step ", result.bestTerminalState[:step])
+println("  Thought: ", result.bestTerminalState[:thought])
+println("  Action: ", result.bestTerminalState[:action])
+println()
+println("Solution complete! ✓")
+println("Root node visits: ", result.root.visits)
+```