Question

Distribute 127 one dollar bills among 7 wallets so that any integer sum from 1 through 127 dollars can be paid without opening the wallets.

Answer 1

127 one dollar bills can be distributed among 7 wallets so that any integer sum from 1 to 127 dollars can be paid without opening the wallets as

2⁰ dollar, 2¹ dollars, 2² dollars, 2³ dollars, 2⁴ dollars, 2⁵ dollars, 2⁶ dollars i.e.,

1 dollar, 2 dollars, 4 dollars, 8 dollars, 16 dollars, 32 dollars, 64 dollars