def find_10_10_tours():
    n = 16
    solutions = []
 
    def backtrack(seq):
        # If we've built a sequence of length 10:
        if len(seq) == n:
            # Check if it ends with 9:
            if seq[-1] == 15:
                solutions.append(seq[:])  # Store a copy of this valid tour
            return
 
        used = set(seq)
 
        # Try all possible next values from 1..10
        for next_val in range(1, n+1):
            if next_val not in used:
                # We only allow next_val if it can be expressed
                # as a_i - a_j for some i,j < current length,
                # with a_i > a_j.
                valid = False
                # For l < 3, we can skip the difference check if l=2?
                # Actually, the problem states "for l >= 3," so for the second position
                # (index 1 in Python), there is no difference requirement yet.
                # We'll handle that condition carefully:
                if len(seq) < 2:
                    # If we haven't placed the second element yet,
                    # there's no difference requirement. We can pick anything not used.
                    valid = True
                else:
                    # Now we must see if next_val is a difference of two earlier terms
                    for i in range(len(seq)):
                        for j in range(len(seq)):
                            if i != j and seq[i] > seq[j]:
                                if seq[i] - seq[j] == next_val:
                                    valid = True
                                    break
                        if valid:
                            break
 
                if valid:
                    seq.append(next_val)
                    backtrack(seq)
                    seq.pop()
 
    # We start the sequence with a1 = 10
    initial_seq = [16]
    backtrack(initial_seq)
 
    return solutions
 
 
# --- Run the search and display results ---
all_tours = find_10_10_tours()
 
print("All (10,10)-tours found (each sequence of length 10):")
for tour in all_tours:
    print(tour)
 
print(f"\nTotal number of (10,10)-tours found: {len(all_tours)}")

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