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The logic followed here is as follows: The square of each digit of the 1st number is added together and then, the resultant is multiplied by 2 to obtain the 2nd number.
268: 208 → [2 × {(2)² + (6)²+ (8)² }] = [2 × {4 + 36 + 64}]= [2 × 104] = 208
552: 102 → [2 × {(5)² + (5)² + (1)² }] = [2 × {25 + 25 + 1}]= [2 × 51] = 102
635: 140 → [2 × {(6)² + (3)² + (5)² }] = [2 × {36 + 9 + 25}]= [2 × 70] = 140
397: 282 → [2 × {(3)² + (9)² + (7)² }] = [2 × {9 + 81 + 49}]= [2 × 139] = 278 ≠ 282
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