The restaurant bill is 25 BTC. The three friends each paid 10 BTC, totaling 30 BTC. The waiter returns 1 BTC to each friend (3 BTC total) and keeps 2 BTC as a tip. Each friend’s net contribution is 10 - 1 = 9 BTC, so the total paid by the friends is 3 × 9 = 27 BTC. This 27 BTC covers the 25 BTC bill plus the 2 BTC tip kept by the waiter (25 + 2 = 27 BTC).
The confusion arises from the misleading step of adding the 2 BTC tip to the 27 BTC paid by the friends to get 29 BTC, then comparing it to the original 30 BTC. The original 30 BTC is no longer relevant after the refund; it’s not supposed to match anything. The correct accounting is:
The restaurant gets 25 BTC (the bill).
The waiter keeps 2 BTC (the tip).
The friends get back 3 BTC (1 BTC each).
Total: 25 + 2 + 3 = 30 BTC, which matches the initial payment.
There’s no missing 1 BTC—it’s an illusion created by the problem’s wording, which tricks you into thinking the 27 BTC paid by the friends plus the 2 BTC tip should equal 30 BTC. Instead, the 27 BTC paid by the friends already includes the 2 BTC tip (25 BTC bill + 2 BTC tip = 27 BTC). The puzzle is a classic accounting misdirection, not a math error.
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