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Number Path: Powers of 2 (2 to 4096)

Fill in the missing numbers. Each number is double the one before it (2, 4, 8, 16, ...). Make one path from 2 to 4096. Consecutive numbers must share a side. Diagonal moves are not allowed. Use each number exactly once.

Example
2 → 4096243264409681612820481024512256
  1. 1.
    2 → 40964409616251264
  2. 2.
    2 → 409640966423284
  3. 3.
    2 → 4096512816128232
  4. 4.
    2 → 4096321282561624096
  5. 5.
    2 → 4096512212840963216
  6. 6.
    2 → 4096241632102464
  7. 7.
    2 → 40962410242563216
  8. 8.
    2 → 409625124096128
  9. 9.
    2 → 409625651224096
  10. 10.
    2 → 4096816264
  11. 11.
    2 → 4096128409624
  12. 12.
    2 → 4096102464216
  13. 13.
    2 → 4096128162512
  14. 14.
    2 → 409622048102464