[OPE-L:1519] Re: quiz

Allin Cottrell (cottrell@wfu.edu)
Mon, 18 Mar 1996 13:03:44 -0800

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Andrew:

> 3 men check into a hotel. The clerk, Nassau Senior, looks up the price,
> \$30. The men sign in. Each hands over a \$10 bill, which Senior records.
>
> Later, the manager looks over the books, and finds that Senior has over-
> charged the men. The price is only \$25. The manager takes 5 \$1 bills out
> of the cash register, and tells Senior to give them to the men.
>
> Senior realizes that 3 men cannot split \$5 evenly, so, on the way to the
> room, he puts \$2 in his pocket and gives the men \$3, telling them the
> price is really \$27.
>
> The men paid \$30, but got back \$3, so ended up paying \$27. Senior has
> \$2 in his pocket. But \$27 + \$2 = \$29. Where's Senior's Last Dollar?

The question implies that the net payment by the guests (\$27) and the
amount pocketed by Senior (\$2) "ought" to add up to the initial payment
made by the guests (\$30), but there's simply no reason for that
supposition. Suppose two guests had paid \$15 each initially, and, on
being asked to return \$5 to them, Senior had handed over \$2 to each guest,
pocketing \$1. In that case the net payment by the guests is \$26, and \$26
+ \$1 = \$27, so "Where are Senior's Last *Three* Dollars" in that case?
Nowhere. There's no problem. In both cases the \$30 paid initially is
divided unmysteriously into the sum remaining in the till, the sum
returned to the guests, and the sum pocketed by Senior; but the net sum
paid by the guests and the sum taken by Senior simply do not constitute a
partitioning of the \$30.

Have I won the right to answer more silly questions?

Allin.