using System;
using System.Collections.Generic;
class Program
{
    struct JyoutaiDef
    {
        internal bool IsALeft;
        internal bool IsBLeft;
        internal bool IsCLeft;
        internal bool IsDLeft;
        internal bool IsELeft;
        internal bool IsTaimatuLeft;
        internal List<string> LogList;
        internal List<int> TimeRunSumList;
        internal void Init()
        {
            IsALeft = IsBLeft = IsCLeft = IsDLeft = IsELeft = true;
            IsTaimatuLeft = true;
            LogList = new List<string>();
            TimeRunSumList = new List<int>() { 0 };
            AddOneLog();
        }
        internal void MakeKishiInfo(bool pIsLeftInfo, System.Text.StringBuilder pSb)
        {
            if (pIsLeftInfo == IsALeft) pSb.Append("A,");
            if (pIsLeftInfo == IsBLeft) pSb.Append("B,");
            if (pIsLeftInfo == IsCLeft) pSb.Append("C,");
            if (pIsLeftInfo == IsDLeft) pSb.Append("D,");
            if (pIsLeftInfo == IsELeft) pSb.Append("E,");
        }
        internal bool AddOneLog()
        {
            var sb = new System.Text.StringBuilder();
            MakeKishiInfo(true, sb);
            sb.Append(IsTaimatuLeft ? " たいまつ 吊り橋 " : " 吊り橋 たいまつ ");
            MakeKishiInfo(false, sb);
            string wkStr = sb.ToString();
            if (LogList.Contains(wkStr)) return false;
            LogList.Add(wkStr);
            return true;
        }
        internal void PrintLog()
        {
            for (int I = 0; I <= LogList.Count - 1; I++) {
                Console.WriteLine("レベル{0} {1} 合計時間={2}", I, LogList[I], TimeRunSumList[I]);
            }
        }
    }
    static void Main()
    {
        var Jyoutai = new JyoutaiDef();
        Jyoutai.Init();
        var que = new Queue<JyoutaiDef>();
        que.Enqueue(Jyoutai);
        int MaxTimeSum = 30;
        int AnswerCnt = 0;
        while (que.Count > 0) {
            Jyoutai = que.Dequeue();
            int CurrTimeRunSum = Jyoutai.TimeRunSumList[Jyoutai.TimeRunSumList.Count - 1];
            if (CurrTimeRunSum > MaxTimeSum)
                continue;
            if (Jyoutai.IsALeft == false && Jyoutai.IsBLeft == false
             && Jyoutai.IsCLeft == false && Jyoutai.IsDLeft == false
             && Jyoutai.IsELeft == false && Jyoutai.IsTaimatuLeft == false) {
                Console.WriteLine("解{0}を発見しました。", ++AnswerCnt);
                Jyoutai.PrintLog();
                MaxTimeSum = CurrTimeRunSum;
                continue;
            }
            Action<JyoutaiDef, int> EnqueueSyori = (pWillEnqueue, pKasanVal) =>
            {
                pWillEnqueue.TimeRunSumList = new List<int>(Jyoutai.TimeRunSumList);
                pWillEnqueue.TimeRunSumList.Add(CurrTimeRunSum + pKasanVal);
                pWillEnqueue.LogList = new List<string>(Jyoutai.LogList);
                pWillEnqueue.IsTaimatuLeft = !Jyoutai.IsTaimatuLeft;
                if (pWillEnqueue.AddOneLog()) que.Enqueue(pWillEnqueue);
            };
            if (Jyoutai.IsTaimatuLeft) {
                //AとBを移動
                if (Jyoutai.IsALeft && Jyoutai.IsBLeft) {
                    JyoutaiDef WillEnqueue = Jyoutai;
                    WillEnqueue.IsALeft = WillEnqueue.IsBLeft = false;
                    EnqueueSyori(WillEnqueue, 3);
                }
                //AとCを移動
                if (Jyoutai.IsALeft && Jyoutai.IsCLeft) {
                    JyoutaiDef WillEnqueue = Jyoutai;
                    WillEnqueue.IsALeft = WillEnqueue.IsCLeft = false;
                    EnqueueSyori(WillEnqueue, 6);
                }
                //AとDを移動
                if (Jyoutai.IsALeft && Jyoutai.IsDLeft) {
                    JyoutaiDef WillEnqueue = Jyoutai;
                    WillEnqueue.IsALeft = WillEnqueue.IsDLeft = false;
                    EnqueueSyori(WillEnqueue, 8);
                }
                //AとEを移動
                if (Jyoutai.IsALeft && Jyoutai.IsELeft) {
                    JyoutaiDef WillEnqueue = Jyoutai;
                    WillEnqueue.IsALeft = WillEnqueue.IsELeft = false;
                    EnqueueSyori(WillEnqueue, 12);
                }
                //BとCを移動
                if (Jyoutai.IsBLeft && Jyoutai.IsCLeft) {
                    JyoutaiDef WillEnqueue = Jyoutai;
                    WillEnqueue.IsBLeft = WillEnqueue.IsCLeft = false;
                    EnqueueSyori(WillEnqueue, 6);
                }
                //BとDを移動
                if (Jyoutai.IsBLeft && Jyoutai.IsDLeft) {
                    JyoutaiDef WillEnqueue = Jyoutai;
                    WillEnqueue.IsBLeft = WillEnqueue.IsDLeft = false;
                    EnqueueSyori(WillEnqueue, 8);
                }
                //BとEを移動
                if (Jyoutai.IsBLeft && Jyoutai.IsELeft) {
                    JyoutaiDef WillEnqueue = Jyoutai;
                    WillEnqueue.IsBLeft = WillEnqueue.IsELeft = false;
                    EnqueueSyori(WillEnqueue, 12);
                }
                //CとDを移動
                if (Jyoutai.IsCLeft && Jyoutai.IsDLeft) {
                    JyoutaiDef WillEnqueue = Jyoutai;
                    WillEnqueue.IsCLeft = WillEnqueue.IsDLeft = false;
                    EnqueueSyori(WillEnqueue, 8);
                }
                //CとEを移動
                if (Jyoutai.IsCLeft && Jyoutai.IsELeft) {
                    JyoutaiDef WillEnqueue = Jyoutai;
                    WillEnqueue.IsCLeft = WillEnqueue.IsELeft = false;
                    EnqueueSyori(WillEnqueue, 12);
                }
                //DとEを移動
                if (Jyoutai.IsDLeft && Jyoutai.IsELeft) {
                    JyoutaiDef WillEnqueue = Jyoutai;
                    WillEnqueue.IsDLeft = WillEnqueue.IsELeft = false;
                    EnqueueSyori(WillEnqueue, 12);
                }
                //Aを移動
                if (Jyoutai.IsALeft) {
                    JyoutaiDef WillEnqueue = Jyoutai;
                    WillEnqueue.IsALeft = false;
                    EnqueueSyori(WillEnqueue, 1);
                }
                //Bを移動
                if (Jyoutai.IsBLeft) {
                    JyoutaiDef WillEnqueue = Jyoutai;
                    WillEnqueue.IsBLeft = false;
                    EnqueueSyori(WillEnqueue, 3);
                }
                //Cを移動
                if (Jyoutai.IsCLeft) {
                    JyoutaiDef WillEnqueue = Jyoutai;
                    WillEnqueue.IsCLeft = false;
                    EnqueueSyori(WillEnqueue, 6);
                }
                //Dを移動
                if (Jyoutai.IsDLeft) {
                    JyoutaiDef WillEnqueue = Jyoutai;
                    WillEnqueue.IsDLeft = false;
                    EnqueueSyori(WillEnqueue, 8);
                }
                //Eを移動
                if (Jyoutai.IsELeft) {
                    JyoutaiDef WillEnqueue = Jyoutai;
                    WillEnqueue.IsELeft = false;
                    EnqueueSyori(WillEnqueue, 12);
                }
            }
            else {
                //AとBを移動
                if (Jyoutai.IsALeft == false && Jyoutai.IsBLeft == false) {
                    JyoutaiDef WillEnqueue = Jyoutai;
                    WillEnqueue.IsALeft = WillEnqueue.IsBLeft = true;
                    EnqueueSyori(WillEnqueue, 3);
                }
                //AとCを移動
                if (Jyoutai.IsALeft == false && Jyoutai.IsCLeft == false) {
                    JyoutaiDef WillEnqueue = Jyoutai;
                    WillEnqueue.IsALeft = WillEnqueue.IsCLeft = true;
                    EnqueueSyori(WillEnqueue, 6);
                }
                //AとDを移動
                if (Jyoutai.IsALeft == false && Jyoutai.IsDLeft == false) {
                    JyoutaiDef WillEnqueue = Jyoutai;
                    WillEnqueue.IsALeft = WillEnqueue.IsDLeft = true;
                    EnqueueSyori(WillEnqueue, 8);
                }
                //AとEを移動
                if (Jyoutai.IsALeft == false && Jyoutai.IsELeft == false) {
                    JyoutaiDef WillEnqueue = Jyoutai;
                    WillEnqueue.IsALeft = WillEnqueue.IsELeft = true;
                    EnqueueSyori(WillEnqueue, 12);
                }
                //BとCを移動
                if (Jyoutai.IsBLeft == false && Jyoutai.IsCLeft == false) {
                    JyoutaiDef WillEnqueue = Jyoutai;
                    WillEnqueue.IsBLeft = WillEnqueue.IsCLeft = true;
                    EnqueueSyori(WillEnqueue, 6);
                }
                //BとDを移動
                if (Jyoutai.IsBLeft == false && Jyoutai.IsDLeft == false) {
                    JyoutaiDef WillEnqueue = Jyoutai;
                    WillEnqueue.IsBLeft = WillEnqueue.IsDLeft = true;
                    EnqueueSyori(WillEnqueue, 8);
                }
                //BとEを移動
                if (Jyoutai.IsBLeft == false && Jyoutai.IsELeft == false) {
                    JyoutaiDef WillEnqueue = Jyoutai;
                    WillEnqueue.IsBLeft = WillEnqueue.IsELeft = true;
                    EnqueueSyori(WillEnqueue, 12);
                }
                //CとDを移動
                if (Jyoutai.IsCLeft == false && Jyoutai.IsDLeft == false) {
                    JyoutaiDef WillEnqueue = Jyoutai;
                    WillEnqueue.IsCLeft = WillEnqueue.IsDLeft = true;
                    EnqueueSyori(WillEnqueue, 8);
                }
                //CとEを移動
                if (Jyoutai.IsCLeft == false && Jyoutai.IsELeft == false) {
                    JyoutaiDef WillEnqueue = Jyoutai;
                    WillEnqueue.IsCLeft = WillEnqueue.IsELeft = true;
                    EnqueueSyori(WillEnqueue, 12);
                }
                //DとEを移動
                if (Jyoutai.IsDLeft == false && Jyoutai.IsELeft == false) {
                    JyoutaiDef WillEnqueue = Jyoutai;
                    WillEnqueue.IsDLeft = WillEnqueue.IsELeft = true;
                    EnqueueSyori(WillEnqueue, 12);
                }
                //Aを移動
                if (Jyoutai.IsALeft == false) {
                    JyoutaiDef WillEnqueue = Jyoutai;
                    WillEnqueue.IsALeft = true;
                    EnqueueSyori(WillEnqueue, 1);
                }
                //Bを移動
                if (Jyoutai.IsBLeft == false) {
                    JyoutaiDef WillEnqueue = Jyoutai;
                    WillEnqueue.IsBLeft = true;
                    EnqueueSyori(WillEnqueue, 3);
                }
                //Cを移動
                if (Jyoutai.IsCLeft == false) {
                    JyoutaiDef WillEnqueue = Jyoutai;
                    WillEnqueue.IsCLeft = true;
                    EnqueueSyori(WillEnqueue, 6);
                }
                //Dを移動
                if (Jyoutai.IsDLeft == false) {
                    JyoutaiDef WillEnqueue = Jyoutai;
                    WillEnqueue.IsDLeft = true;
                    EnqueueSyori(WillEnqueue, 8);
                }
                //Eを移動
                if (Jyoutai.IsELeft == false) {
                    JyoutaiDef WillEnqueue = Jyoutai;
                    WillEnqueue.IsELeft = true;
                    EnqueueSyori(WillEnqueue, 12);
                }
            }
        }
    }
}
省略
解7を発見しました。
レベル0 A,B,C,D,E, たいまつ 吊り橋  合計時間=0
レベル1 B,D,E, 吊り橋 たいまつ A,C, 合計時間=6
レベル2 A,B,D,E, たいまつ 吊り橋 C, 合計時間=7
レベル3 D,E, 吊り橋 たいまつ A,B,C, 合計時間=10
レベル4 A,D,E, たいまつ 吊り橋 B,C, 合計時間=11
レベル5 A, 吊り橋 たいまつ B,C,D,E, 合計時間=23
レベル6 A,B, たいまつ 吊り橋 C,D,E, 合計時間=26
レベル7  吊り橋 たいまつ A,B,C,D,E, 合計時間=29
解8を発見しました。
レベル0 A,B,C,D,E, たいまつ 吊り橋  合計時間=0
レベル1 B,D,E, 吊り橋 たいまつ A,C, 合計時間=6
レベル2 A,B,D,E, たいまつ 吊り橋 C, 合計時間=7
レベル3 D,E, 吊り橋 たいまつ A,B,C, 合計時間=10
レベル4 B,D,E, たいまつ 吊り橋 A,C, 合計時間=13
レベル5 B, 吊り橋 たいまつ A,C,D,E, 合計時間=25
レベル6 A,B, たいまつ 吊り橋 C,D,E, 合計時間=26
レベル7  吊り橋 たいまつ A,B,C,D,E, 合計時間=29