PUZZLE #4459: Plumb Puzzle (diff 1)

plumb learn difficulty: 1/7 simulate author: system unsolved

A hidden plumbing network spells a 4-letter word. Water flows through connected pipes but drains at certain junctions. Find the correct inlet, trace the flow, and decode the 3x5 bitmap pattern.

DATA

Difficulty	`1`
Char Count	`4`
Grid Width	`15`
Grid Height	`5`
Char Width	`3`
Char Height	`5`
Char Gap	`1`
Pipes	{'id': 0, 'row': 4, 'col': 0, 'connections': [15, 28]}, {'id': 1, 'row': 4, 'col': 3, 'connections': [14, 30]}, {'id': 2, 'row': 4, 'col': 6, 'connections': [16, 29]}, {'id': 3, 'row': 4, 'col': 12, 'connections': [19, 33]}, {'id': 4, 'row': 3, 'col': 10, 'connections': [25, 31, 38]}, {'id': 5, 'row': 0, 'col': 5, 'connections': [21, 23, 36]}, {'id': 6, 'row': 1, 'col': 0, 'connections': [34, 35]}, {'id': 7, 'row': 0, 'col': 8, 'connections': [10, 20, 26]}, {'id': 8, 'row': 2, 'col': 5, 'connections': [23, 29]}, {'id': 9, 'row': 0, 'col': 14, 'connections': [24]}, {'id': 10, 'row': 1, 'col': 9, 'connections': [7, 12, 22, 25, 26, 38, 40]}, {'id': 11, 'row': 0, 'col': 11, 'connections': [13, 22, 37, 40]}, {'id': 12, 'row': 2, 'col': 8, 'connections': [10, 26, 32, 38]}, {'id': 13, 'row': 1, 'col': 12, 'connections': [11, 24, 27, 37, 39]}, {'id': 14, 'row': 4, 'col': 2, 'connections': [1, 28]}, {'id': 15, 'row': 3, 'col': 0, 'connections': [0, 28, 35]}, {'id': 16, 'row': 4, 'col': 5, 'connections': [2, 29, 30]}, {'id': 17, 'row': 4, 'col': 8, 'connections': [32]}, {'id': 18, 'row': 4, 'col': 14, 'connections': [33]}, {'id': 19, 'row': 3, 'col': 12, 'connections': [3, 27, 33, 39]}, {'id': 20, 'row': 0, 'col': 7, 'connections': [7, 26, 36]}, {'id': 21, 'row': 0, 'col': 4, 'connections': [5, 23]}, {'id': 22, 'row': 0, 'col': 10, 'connections': [10, 11, 40]}, {'id': 23, 'row': 1, 'col': 5, 'connections': [5, 8, 21, 36]}, {'id': 24, 'row': 0, 'col': 13, 'connections': [9, 13, 37]}, {'id': 25, 'row': 2, 'col': 10, 'connections': [4, 10, 38, 40]}, {'id': 26, 'row': 1, 'col': 8, 'connections': [7, 10, 12, 20, 38]}, {'id': 27, 'row': 2, 'col': 13, 'connections': [13, 19, 39]}, {'id': 28, 'row': 4, 'col': 1, 'connections': [0, 14, 15]}, {'id': 29, 'row': 3, 'col': 5, 'connections': [2, 8, 16, 30]}, {'id': 30, 'row': 4, 'col': 4, 'connections': [1, 16, 29]}, {'id': 31, 'row': 4, 'col': 10, 'connections': [4]}, {'id': 32, 'row': 3, 'col': 8, 'connections': [12, 17, 38]}, {'id': 33, 'row': 4, 'col': 13, 'connections': [3, 18, 19]}, {'id': 34, 'row': 0, 'col': 0, 'connections': [6]}, {'id': 35, 'row': 2, 'col': 0, 'connections': [6, 15]}, {'id': 36, 'row': 0, 'col': 6, 'connections': [5, 20, 23]}, {'id': 37, 'row': 0, 'col': 12, 'connections': [11, 13, 24]}, {'id': 38, 'row': 2, 'col': 9, 'connections': [4, 10, 12, 25, 26, 32, 40]}, {'id': 39, 'row': 2, 'col': 12, 'connections': [13, 19, 27]}, {'id': 40, 'row': 1, 'col': 10, 'connections': [10, 11, 22, 25, 38]}, {'id': 41, 'row': 0, 'col': 3, 'connections': [42]}, {'id': 42, 'row': 0, 'col': 2, 'connections': [41, 43]}, {'id': 43, 'row': 1, 'col': 2, 'connections': [42, 44]}, {'id': 44, 'row': 2, 'col': 2, 'connections': [43]}, {'id': 45, 'row': 1, 'col': 6, 'connections': [46]}, {'id': 46, 'row': 2, 'col': 6, 'connections': [45, 47, 49]}, {'id': 47, 'row': 2, 'col': 7, 'connections': [46, 48]}, {'id': 48, 'row': 3, 'col': 7, 'connections': [47, 49]}, {'id': 49, 'row': 3, 'col': 6, 'connections': [46, 48]}
Drains	`44, 49`
Inlets	{ "0": 34, "1": 41, "2": 45 }
Font	{ "A": [ "010", "101", "111", "101", "101" ], "B": [ "110", "101", "110", "101", "110" ], "C": [ "011", "100", "100", "100", "011" ], "D": [ "110", "101", "101", "101", "110" ], "E": [ "111", "100", "110", "100", "111" ], "F": [ "111", "100", "110", "100", "100" ], "G": [ "011", "100", "101", "101", "011" ], "H": [ "101", "101", "111", "101", "101" ], "I": [ "111", "010", "010", "010", "111" ], "J": [ "111", "010", "010", "010", "110" ], "K": [ "101", "101", "110", "101", "101" ], "L": [ "100", "100", "100", "100", "111" ], "M": [ "101", "111", "101", "101", "101" ], "N": [ "101", "111", "111", "101", "101" ], "O": [ "010", "101", "101", "101", "010" ], "P": [ "110", "101", "110", "100", "100" ], "Q": [ "010", "101", "101", "110", "011" ], "R": [ "110", "101", "110", "101", "101" ], "S": [ "011", "100", "010", "001", "110" ], "T": [ "111", "010", "010", "010", "010" ], "U": [ "101", "101", "101", "101", "010" ], "V": [ "101", "101", "101", "010", "010" ], "W": [ "101", "101", "101", "111", "101" ], "X": [ "101", "010", "010", "010", "101" ], "Y": [ "101", "010", "010", "010", "010" ], "Z": [ "111", "001", "010", "100", "111" ] }
Instructions	1. Simulate water flow from each inlet (BFS through the pipe graph) 2. Flow stops at drain nodes — water reaching a drain is lost 3. Each inlet fills a set of pipe segments 4. The correct inlet fills pipes that spell a word in 3x5 bitmap font 5. Decode the filled pipe pattern: each character is 3 cols wide, 5 rows tall 6. Grid rows 0..4, each character at col offset = ci * (char_width + char_gap) 7. A pipe cell with row=r and col=c is 'on' for the bitmap 8. Match the 3x5 pattern against the provided font reference
Hint	`The pipe network has 3 inlets and 2 drains. Only one inlet fills the letter-shaped pipes without hitting a drain. Simulate BFS flow from each inlet to find it.`
Answer Format	`lowercase word, no spaces or punctuation`

{
  "type": "plumb",
  "difficulty": 1,
  "char_count": 4,
  "grid_width": 15,
  "grid_height": 5,
  "char_width": 3,
  "char_height": 5,
  "char_gap": 1,
  "pipes": [
    {
      "id": 0,
      "row": 4,
      "col": 0,
      "connections": [
        15,
        28
      ]
    },
    {
      "id": 1,
      "row": 4,
      "col": 3,
      "connections": [
        14,
        30
      ]
    },
    {
      "id": 2,
      "row": 4,
      "col": 6,
      "connections": [
        16,
        29
      ]
    },
    {
      "id": 3,
      "row": 4,
      "col": 12,
      "connections": [
        19,
        33
      ]
    },
    {
      "id": 4,
      "row": 3,
      "col": 10,
      "connections": [
        25,
        31,
        38
      ]
    },
    {
      "id": 5,
      "row": 0,
      "col": 5,
      "connections": [
        21,
        23,
        36
      ]
    },
    {
      "id": 6,
      "row": 1,
      "col": 0,
      "connections": [
        34,
        35
      ]
    },
    {
      "id": 7,
      "row": 0,
      "col": 8,
      "connections": [
        10,
        20,
        26
      ]
    },
    {
      "id": 8,
      "row": 2,
      "col": 5,
      "connections": [
        23,
        29
      ]
    },
    {
      "id": 9,
      "row": 0,
      "col": 14,
      "connections": [
        24
      ]
    },
    {
      "id": 10,
      "row": 1,
      "col": 9,
      "connections": [
        7,
        12,
        22,
        25,
        26,
        38,
        40
      ]
    },
    {
      "id": 11,
      "row": 0,
      "col": 11,
      "connections": [
        13,
        22,
        37,
        40
      ]
    },
    {
      "id": 12,
      "row": 2,
      "col": 8,
      "connections": [
        10,
        26,
        32,
        38
      ]
    },
    {
      "id": 13,
      "row": 1,
      "col": 12,
      "connections": [
        11,
        24,
        27,
        37,
        39
      ]
    },
    {
      "id": 14,
      "row": 4,
      "col": 2,
      "connections": [
        1,
        28
      ]
    },
    {
      "id": 15,
      "row": 3,
      "col": 0,
      "connections": [
        0,
        28,
        35
      ]
    },
    {
      "id": 16,
      "row": 4,
      "col": 5,
      "connections": [
        2,
        29,
        30
      ]
    },
    {
      "id": 17,
      "row": 4,
      "col": 8,
      "connections": [
        32
      ]
    },
    {
      "id": 18,
      "row": 4,
      "col": 14,
      "connections": [
        33
      ]
    },
    {
      "id": 19,
      "row": 3,
      "col": 12,
      "connections": [
        3,
        27,
        33,
        39
      ]
    },
    {
      "id": 20,
      "row": 0,
      "col": 7,
      "connections": [
        7,
        26,
        36
      ]
    },
    {
      "id": 21,
      "row": 0,
      "col": 4,
      "connections": [
        5,
        23
      ]
    },
    {
      "id": 22,
      "row": 0,
      "col": 10,
      "connections": [
        10,
        11,
        40
      ]
    },
    {
      "id": 23,
      "row": 1,
      "col": 5,
      "connections": [
        5,
        8,
        21,
        36
      ]
    },
    {
      "id": 24,
      "row": 0,
      "col": 13,
      "connections": [
        9,
        13,
        37
      ]
    },
    {
      "id": 25,
      "row": 2,
      "col": 10,
      "connections": [
        4,
        10,
        38,
        40
      ]
    },
    {
      "id": 26,
      "row": 1,
      "col": 8,
      "connections": [
        7,
        10,
        12,
        20,
        38
      ]
    },
    {
      "id": 27,
      "row": 2,
      "col": 13,
      "connections": [
        13,
        19,
        39
      ]
    },
    {
      "id": 28,
      "row": 4,
      "col": 1,
      "connections": [
        0,
        14,
        15
      ]
    },
    {
      "id": 29,
      "row": 3,
      "col": 5,
      "connections": [
        2,
        8,
        16,
        30
      ]
    },
    {
      "id": 30,
      "row": 4,
      "col": 4,
      "connections": [
        1,
        16,
        29
      ]
    },
    {
      "id": 31,
      "row": 4,
      "col": 10,
      "connections": [
        4
      ]
    },
    {
      "id": 32,
      "row": 3,
      "col": 8,
      "connections": [
        12,
        17,
        38
      ]
    },
    {
      "id": 33,
      "row": 4,
      "col": 13,
      "connections": [
        3,
        18,
        19
      ]
    },
    {
      "id": 34,
      "row": 0,
      "col": 0,
      "connections": [
        6
      ]
    },
    {
      "id": 35,
      "row": 2,
      "col": 0,
      "connections": [
        6,
        15
      ]
    },
    {
      "id": 36,
      "row": 0,
      "col": 6,
      "connections": [
        5,
        20,
        23
      ]
    },
    {
      "id": 37,
      "row": 0,
      "col": 12,
      "connections": [
        11,
        13,
        24
      ]
    },
    {
      "id": 38,
      "row": 2,
      "col": 9,
      "connections": [
        4,
        10,
        12,
        25,
        26,
        32,
        40
      ]
    },
    {
      "id": 39,
      "row": 2,
      "col": 12,
      "connections": [
        13,
        19,
        27
      ]
    },
    {
      "id": 40,
      "row": 1,
      "col": 10,
      "connections": [
        10,
        11,
        22,
        25,
        38
      ]
    },
    {
      "id": 41,
      "row": 0,
      "col": 3,
      "connections": [
        42
      ]
    },
    {
      "id": 42,
      "row": 0,
      "col": 2,
      "connections": [
        41,
        43
      ]
    },
    {
      "id": 43,
      "row": 1,
      "col": 2,
      "connections": [
        42,
        44
      ]
    },
    {
      "id": 44,
      "row": 2,
      "col": 2,
      "connections": [
        43
      ]
    },
    {
      "id": 45,
      "row": 1,
      "col": 6,
      "connections": [
        46
      ]
    },
    {
      "id": 46,
      "row": 2,
      "col": 6,
      "connections": [
        45,
        47,
        49
      ]
    },
    {
      "id": 47,
      "row": 2,
      "col": 7,
      "connections": [
        46,
        48
      ]
    },
    {
      "id": 48,
      "row": 3,
      "col": 7,
      "connections": [
        47,
        49
      ]
    },
    {
      "id": 49,
      "row": 3,
      "col": 6,
      "connections": [
        46,
        48
      ]
    }
  ],
  "drains": [
    44,
    49
  ],
  "inlets": {
    "0": 34,
    "1": 41,
    "2": 45
  },
  "font": {
    "A": [
      "010",
      "101",
      "111",
      "101",
      "101"
    ],
    "B": [
      "110",
      "101",
      "110",
      "101",
      "110"
    ],
    "C": [
      "011",
      "100",
      "100",
      "100",
      "011"
    ],
    "D": [
      "110",
      "101",
      "101",
      "101",
      "110"
    ],
    "E": [
      "111",
      "100",
      "110",
      "100",
      "111"
    ],
    "F": [
      "111",
      "100",
      "110",
      "100",
      "100"
    ],
    "G": [
      "011",
      "100",
      "101",
      "101",
      "011"
    ],
    "H": [
      "101",
      "101",
      "111",
      "101",
      "101"
    ],
    "I": [
      "111",
      "010",
      "010",
      "010",
      "111"
    ],
    "J": [
      "111",
      "010",
      "010",
      "010",
      "110"
    ],
    "K": [
      "101",
      "101",
      "110",
      "101",
      "101"
    ],
    "L": [
      "100",
      "100",
      "100",
      "100",
      "111"
    ],
    "M": [
      "101",
      "111",
      "101",
      "101",
      "101"
    ],
    "N": [
      "101",
      "111",
      "111",
      "101",
      "101"
    ],
    "O": [
      "010",
      "101",
      "101",
      "101",
      "010"
    ],
    "P": [
      "110",
      "101",
      "110",
      "100",
      "100"
    ],
    "Q": [
      "010",
      "101",
      "101",
      "110",
      "011"
    ],
    "R": [
      "110",
      "101",
      "110",
      "101",
      "101"
    ],
    "S": [
      "011",
      "100",
      "010",
      "001",
      "110"
    ],
    "T": [
      "111",
      "010",
      "010",
      "010",
      "010"
    ],
    "U": [
      "101",
      "101",
      "101",
      "101",
      "010"
    ],
    "V": [
      "101",
      "101",
      "101",
      "010",
      "010"
    ],
    "W": [
      "101",
      "101",
      "101",
      "111",
      "101"
    ],
    "X": [
      "101",
      "010",
      "010",
      "010",
      "101"
    ],
    "Y": [
      "101",
      "010",
      "010",
      "010",
      "010"
    ],
    "Z": [
      "111",
      "001",
      "010",
      "100",
      "111"
    ]
  },
  "instructions": "1. Simulate water flow from each inlet (BFS through the pipe graph)\n2. Flow stops at drain nodes \u2014 water reaching a drain is lost\n3. Each inlet fills a set of pipe segments\n4. The correct inlet fills pipes that spell a word in 3x5 bitmap font\n5. Decode the filled pipe pattern: each character is 3 cols wide, 5 rows tall\n6. Grid rows 0..4, each character at col offset = ci * (char_width + char_gap)\n7. A pipe cell with row=r and col=c is 'on' for the bitmap\n8. Match the 3x5 pattern against the provided font reference",
  "hint": "The pipe network has 3 inlets and 2 drains. Only one inlet fills the letter-shaped pipes without hitting a drain. Simulate BFS flow from each inlet to find it.",
  "answer_format": "lowercase word, no spaces or punctuation"
}

author's note: Pool fill: plumb diff 1