# Can anyone explain 'The Missing Dollar' Conundrum, please?

This was on the Simon Mayo R2 show this evening. I understood the maths of the problem, but not the answer that was given.

The story is that three men check into a hotel for the night. The room rate is \$30, so they pay \$10 each. Once they've gone up to the room, the receptionist realises that he's overcharged them as the room rate should only be \$25. Because they've paid separately, he realise he can't refund them equally, so he gives them back one dollar each and pockets the other two himself.

So now they've each paid \$9 dollars for the room, a total of \$27, and the receptionist has kept \$2, making \$29 in all. So where's the missing dollar?

The guy on the radio explained why this thinking was mathematically wrong, but I couldn't get my head round it. Can anyone explain in idiot language, please?
18:42 Tue 08th May 2012
 HowardKennitby There is no missing dollar The hotel has \$25 The guests have \$1 each and the receptionist has \$2. Total = \$30 18:44 Tue 08th May 2012 Go To Best Answer

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 they haven't paid \$9, they've all paid \$9 & 2/3 (two third dollars) 18:44 Tue 08th May 2012 There is no missing dollar The hotel has \$25 The guests have \$1 each and the receptionist has \$2. Total = \$30 18:44 Tue 08th May 2012 The fallacy is that they have not paid \$9 for the room but \$8.33. They have paid \$9 for the room plus what the receptionist has pocketed. 18:45 Tue 08th May 2012 It's a nonsensical calculation because there is absolutely no logic in adding the 27 to the 2. The hotel has \$25, the receptionist has \$2 and the men have \$3- so all \$30 is accounted for. 18:46 Tue 08th May 2012 The three guys have each paid \$9, which is \$27 all right, but the \$2 that the receptionist kept is PART OF that \$27. So if you add it instead of subtracting it, you get \$29 which completely illogically consists of \$25 plus another \$2 counted twice. Since that's an illogical sum, then whatever you try to compare it with, it is sure to turn out nonsense of one kind or another. 18:49 Tue 08th May 2012 I remember this one from my childhood, only it was three men in a restaurant paying for their meal. This was before decimal currency when a pound was exactly divisible by three. 18:50 Tue 08th May 2012 Question Author Of course I knew that really..... Seriously, thanks everyone. That was driving me nuts. I'm not at all good with numbers, but I think I've got it now. 18:51 Tue 08th May 2012 \$30-3=27-2=25 no missing \$ 18:52 Tue 08th May 2012

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