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Here's how I checked my work with the 382 solution:
Start with 382.
Give away 1/2 (191) + 1 = 192
Left with 190.
Give away 1/2 (95) + 1 = 96
Left with 94.
Give away 1/2 (47) + 1 = 48
Left with 46.
Give away 1/2 (23) + 1 = 24
Left with 22.
Give away 1/2 (11) + 1 = 12
Left with 10.
Give away 1/2 (5) + 1 = 6
Left with 4.
Give away 1/2 (2) + 1 = 3
Left with 1.
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