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I have come across a puzzle, which makes no sense. Does anyone know the answer to the below?

You and two friends go on holiday. When checking out, the total bill comes to £300. You pay the bill and begin to walk out. The clerk realises that he’s made an error and hands the bellhop a £50 note to return to you. He realises that he cannot split the £50 equally, so he decides to give each guest £10 and keep £20 as a tip for himself. Hence, each guest received £10 back, meaning they only paid £90 each. This means the total paid by the three people was £270 (£90 x 3). Add in the £20 the bellhop kept and the total comes to £290. What happened to the missing £10?

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  • $\begingroup$ Not only is it a duplicate, there's even another question about where it came from. This version is closer to the original but it's still a duplicate on Puzzling. $\endgroup$
    – Engineer Toast
    Commented Jun 24, 2015 at 12:22

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You should be deducting the Bellhop's £20 from the £270, not adding it.

Edited with more details: The question is deliberately misleading you into thinking there's a paradox, and some money has gone missing.

The total amount paid initially was £300, £100 each.

The total amount paid after the partial refund was £270, £90 each.

The sly bellhop kept the final £20 for himself - had he split this evenly, the total amount paid would have been £250 - £83.333... each.

The question is misleading in the way it deducts the refund received by the customers, but then attempts to add the refund stolen by the bellhop.

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    $\begingroup$ Welcome to Puzzling! The idea looks correct, could you please add more details to your answer? Solutions with scarce explanation are likely to be deleted, even if upvoted. $\endgroup$
    – leoll2
    Commented Jun 24, 2015 at 11:54
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Let's consider the total amounts of money.

BEFORE PAYING:

Guests: 300 (3x100)
Clerk: 0
Shop: 0

The clerk gets a 20 tip, while each man pays 90 (gives 100 but is returned 10).

AFTER PAYING:

Guests: 30 (3x10)
Clerk: 20
Shop: 250

As you can see there is no paradox, the only mistake was trying to sum 20 to 270 which absolutely makes no sense!

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You pay £300.
The clerk returns £50.
The bellhop returns £30 of the £50 and keeps £20.
You and your friends have paid £270.
The clerk intended for you to have paid £250.

£300 = £250 + £50(change)
£50 = £10 + £10 + £10 (returned to you) + £20 (kept by bellhop)

I'm not sure where you see a missing £10, so I can't tell you what happened to it.

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