|
| 1 | +// Each block's parameters |
| 2 | +const blocks = [ |
| 3 | + { divZ: 1, addX: 14, addY: 0 }, // 0 |
| 4 | + { divZ: 1, addX: 13, addY: 12 }, // 1 |
| 5 | + { divZ: 1, addX: 15, addY: 14 }, // 2 |
| 6 | + { divZ: 1, addX: 13, addY: 0 }, // 3 |
| 7 | + { divZ: 26, addX: -2, addY: 3 }, // 4 |
| 8 | + { divZ: 1, addX: 10, addY: 15 }, // 5 |
| 9 | + { divZ: 1, addX: 13, addY: 11 }, // 6 |
| 10 | + { divZ: 26, addX: -15, addY: 12 }, // 7 |
| 11 | + { divZ: 1, addX: 11, addY: 1 }, // 8 |
| 12 | + { divZ: 26, addX: -9, addY: 12 }, // 9 |
| 13 | + { divZ: 26, addX: -9, addY: 3 }, // 10 |
| 14 | + { divZ: 26, addX: -7, addY: 10 }, // 11 |
| 15 | + { divZ: 26, addX: -4, addY: 14 }, // 12 |
| 16 | + { divZ: 26, addX: -6, addY: 12 } // 13 |
| 17 | +]; |
| 18 | + |
| 19 | +function findRelationships() { |
| 20 | + let stack = []; |
| 21 | + let relationships = []; |
| 22 | + |
| 23 | + for (let i = 0; i < blocks.length; i++) { |
| 24 | + if (blocks[i].divZ === 1) { |
| 25 | + stack.push({ pos: i, value: blocks[i].addY }); |
| 26 | + } else { |
| 27 | + const prev = stack.pop(); |
| 28 | + relationships.push({ |
| 29 | + pos1: prev.pos, |
| 30 | + pos2: i, |
| 31 | + diff: prev.value + blocks[i].addX |
| 32 | + }); |
| 33 | + } |
| 34 | + } |
| 35 | + return relationships; |
| 36 | +} |
| 37 | + |
| 38 | +function findAllValidPairs(diff) { |
| 39 | + const pairs = []; |
| 40 | + for (let w1 = 1; w1 <= 9; w1++) { |
| 41 | + const w2 = w1 + diff; |
| 42 | + if (w2 >= 1 && w2 <= 9) { |
| 43 | + pairs.push([w1, w2]); |
| 44 | + } |
| 45 | + } |
| 46 | + return pairs; |
| 47 | +} |
| 48 | + |
| 49 | +function* generateAllValidNumbers(relationships, currentDigits = new Array(14).fill(null), relationshipIndex = 0) { |
| 50 | + if (relationshipIndex === relationships.length) { |
| 51 | + // Fill in any remaining unassigned digits with 9 (for maximum) or 1 (for minimum) |
| 52 | + const result = [...currentDigits]; |
| 53 | + for (let i = 0; i < result.length; i++) { |
| 54 | + if (result[i] === null) { |
| 55 | + result[i] = 9; // or 1 for minimum |
| 56 | + } |
| 57 | + } |
| 58 | + yield result; |
| 59 | + return; |
| 60 | + } |
| 61 | + |
| 62 | + const rel = relationships[relationshipIndex]; |
| 63 | + const validPairs = findAllValidPairs(rel.diff); |
| 64 | + |
| 65 | + for (const [w1, w2] of validPairs) { |
| 66 | + if ((currentDigits[rel.pos1] === null || currentDigits[rel.pos1] === w1) && |
| 67 | + (currentDigits[rel.pos2] === null || currentDigits[rel.pos2] === w2)) { |
| 68 | + const nextDigits = [...currentDigits]; |
| 69 | + nextDigits[rel.pos1] = w1; |
| 70 | + nextDigits[rel.pos2] = w2; |
| 71 | + yield* generateAllValidNumbers(relationships, nextDigits, relationshipIndex + 1); |
| 72 | + } |
| 73 | + } |
| 74 | +} |
| 75 | + |
| 76 | +function verifyNumber(digits) { |
| 77 | + let z = 0; |
| 78 | + for (let i = 0; i < 14; i++) { |
| 79 | + const w = digits[i]; |
| 80 | + let x = z % 26; |
| 81 | + z = Math.floor(z / blocks[i].divZ); |
| 82 | + x += blocks[i].addX; |
| 83 | + x = (x === w) ? 0 : 1; |
| 84 | + const y = (w + blocks[i].addY) * x; |
| 85 | + z = z * (25 * x + 1) + y; |
| 86 | + } |
| 87 | + return z === 0; |
| 88 | +} |
| 89 | + |
| 90 | +// Find all valid numbers |
| 91 | +function findAllValidNumbers() { |
| 92 | + const relationships = findRelationships(); |
| 93 | + const validNumbers = []; |
| 94 | + |
| 95 | + console.log('Digit relationships:'); |
| 96 | + relationships.forEach(rel => { |
| 97 | + console.log(`digit[${rel.pos1}] + ${rel.diff} = digit[${rel.pos2}]`); |
| 98 | + }); |
| 99 | + |
| 100 | + console.log('\nSearching for valid numbers...'); |
| 101 | + for (const digits of generateAllValidNumbers(relationships)) { |
| 102 | + if (verifyNumber(digits)) { |
| 103 | + validNumbers.push([...digits]); |
| 104 | + } |
| 105 | + } |
| 106 | + |
| 107 | + // Sort numbers for better display |
| 108 | + validNumbers.sort((a, b) => { |
| 109 | + const numA = BigInt(a.join('')); |
| 110 | + const numB = BigInt(b.join('')); |
| 111 | + return numA < numB ? -1 : numA > numB ? 1 : 0; |
| 112 | + }); |
| 113 | + |
| 114 | + return validNumbers; |
| 115 | +} |
| 116 | + |
| 117 | +// Find and display all solutions |
| 118 | +const allValidNumbers = findAllValidNumbers(); |
| 119 | +console.log(`\nFound ${allValidNumbers.length} valid numbers:`); |
| 120 | +console.log('Smallest:', allValidNumbers[0].join('')); |
| 121 | +console.log('Largest:', allValidNumbers[allValidNumbers.length - 1].join('')); |
| 122 | +console.log('\nAll valid numbers:'); |
| 123 | +allValidNumbers.forEach(digits => console.log(digits.join(''))); |
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